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IGNOU BMTC 132 SOLVED ASSIGNMENT HINDI

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IGNOU BMTC 132 SOLVED ASSIGNMENT HINDI

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Last Date of Submission of IGNOU BMTC-132 (BSCG) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).
Semester Wise
January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam).
July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

Title Name	IGNOU BMTC 132 SOLVED ASSIGNMENT HINDI
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSCG
Course Name	Bachelor of Science
Subject Code	BMTC 132
Subject Name	Differential Equations
Year	2026
Session
Language	English Medium
Assignment Code	BMTC-132/Assignmentt-1//2026
Product Description	Assignment of BSCG (Bachelor of Science) 2026. Latest BMTC 132 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BMTC-132 (BSCG) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam). Semester Wise January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

~~Rs. 80~~
Rs. 41

Questions Included in this Help Book

Ques 1.

बताइए कि निम्नलिखित कथन सत्य हैं या असत्य। संक्षिप्त उपपत्ति अथवा प्रत्युदाहरण की सहायता से अपने उत्तर की पुष्टि कीजिए :
क) y² अवकल समीकरण :
$$6xy \, dx + (4y + 9x^2)dy = 0$ $
का समाकलन गुणक है।
ख) अवकल समीकरण $\frac{dy}{d} = y$ , जहाँ $y(0) = 0$ , के हल का अस्तित्व है लेकिन हल अद्वितीय नहीं है।
ग) अंतराल $]0, \pi[$ में समीकरण : $\sin x \frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0$ समघात रैखिक समीकरण है।
घ) अवकल समीकरण
$$\frac{dy}{dx} = y, \quad y(0) = 0$ $
के हल का अस्तित्व है, परंतु हल अद्वितीय नहीं है।
ङ) फैफियन अवकल समीकरण $(2xy^2 + 2xy + 2xz^2 + 1)dx + dy + 2z \, dz = 0$ समाकलनीय है।

Ques 2.

अवकल समीकरण :

$$y'' + 6y' + 9y = \frac{1}{x^3}e^{-3x}, \text{ x} > 0.$ $
को प्राचल विचरण विधि से हल कीजिए।

Ques 3.

मान लीजिए एक थर्मामीटर जिसके घर के अंदर रीडिंग $75^{\circ}\text{F}$ है, उसे बाहर रखा जाता है, जहाँ वायु तापमान $15^{\circ}\text{F}$ है। दो मिनट के बाद थर्मामीटर की रीडिंग $30^{\circ}\text{F}$ पाई जाती है। किसी भी समय t पर थर्मामीटर के तापमान की रीडिंग T(t) ज्ञात कीजिए।

Ques 4.

आंशिक अवकल समीकरण :
$$(x - y)p + (y - x - z)q = z$ $
का समाकल पृष्ठ ज्ञात कीजिए जो वृत्त $z = 1, x^2 + y^2 = 1$ से गुजरता हो।

Ques 5.

हल कीजिए : $(x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0$ . $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(5)$

Ques 6.

हल कीजिए : $(x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0$ . $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(5)$

Ques 7.

अनिर्धारित गुणांक विधि से अवकल समीकरण :
$$(D^3 + 2D^2 - D - 2)y = e^x + x^2.$ $
को हल कीजिए। (4)

Ques 8.

अवकल समीकरण $\frac{dy}{dx} = (x + y)^2$ को हल कीजिए।

Ques 9.

अवकल समीकरण $\frac{dy}{dx} = (x + y)^2$ को हल कीजिए। एक कण विरामावस्था से एक माध्यम, जिसमें प्रतिरोध $\lambda v^2$ प्रति इकाई द्रव्यमान है, में नीचे गिरता है। v किसी भी समय t पर कण का वेग है। सिद्ध कीजिए कि कण द्वारा समय t में तय की गई दूरी $\frac{1}{\lambda} \ln \cosh (t \sqrt{g\lambda})$ है, जहाँ g गुरुत्वीय त्वरण है।

Ques 10.

हल कीजिए : $(y^2 + yz)dx + (z^2 + zx)dy + (y^2 - xy)dz = 0.$

Ques 11.

हल कीजिए : $(D^2 + 5DD' + 5D'^2)z = x \sin (3x - 2y).$

Ques 12.

) हल कीजिए : $\frac{dx}{y^2 + yz + z^2} = \frac{dy}{z^2 + zx + x^2} = \frac{dz}{x^2 + xy + y^2}.$

Ques 13.

प्राचल विचरण विधि द्वारा समीकरण
$$\frac{d^2y}{dx^2} + a^2 y = \sec ax$ $
का हल प्राप्त कीजिए। $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$

Ques 14.

चार्पिट विधि द्वारा समीकरण $(p + q)(px + qy) = 1$ का हल प्राप्त कीजिए। $\quad\quad\quad\quad\quad$

Ques 15.

हल कीजिए : $\frac{dy}{dx} = \frac{1}{x + y + 1}.$ $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$ (2)

Ques 16.

हल कीजिए : $(D^2 - DD' - 2D) z = \sin(3x + 4y) + e^{2x+y}.$ $\quad\quad\quad\quad\quad\quad\quad\quad$

Ques 17.

प्राचल विचरण विधि से निम्नलिखित अवकल समीकरण: $y'' - 2y' + y = \frac{12e^x}{x^3}$ को हल कीजिए। $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$

Ques 18.

State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter example: $(5 \times 2 = 10)$
a) y² is an integrating factor of the differential equation:

$6xy \, dx + (4y + 9x^2) \, dy = 0$ .

Ques 19.

The solution of the differential equation $\frac{dy}{d} = y$ with $y(0) = 0$ exists, but is not unique.

Ques 20.

$\sin x \frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0$ in $]0, \pi[$ is a linear homogeneous equation

Ques 21.

The solution of the differential equation

$\frac{dy}{dx} = y$ with $y(0) = 0$

exists, but is not unique.

Ques 22.

The Pfaffian equation $(2xy^2 + 2xy + 2xz^2 + 1)dx + dy + 2z \, dz = 0$ is integrable.

Ques 23.

Apply the method of variation of parameter to solve the differential equation:

$$y'' + 6y' + 9y = \frac{1}{x^3} e^{-3x}, \quad x > 0.$

Ques 24.

Suppose that a thermometer having a reading of $75^\circ\text{F}$ inside a house is placed outside where the air temperature is $15^\circ\text{F}$ . Two minutes later it is found that the thermometer reading is $30^\circ\text{F}$ . Find the temperature reading T(t) of the thermometer at any time t.

Ques 25.

Find the integral surface of the p.d.e.:

$$(x - y)p + (y - x - z)q = z$

through the circle $z = 1, x^2 + y^2 = 1$ .

Ques 26.

Solve: $(x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0$ .

Ques 27.

Using Charpit's method, find the complete integral of the p.d.e.:

$$2xz - px^2 - 2qxy + pq = 0.$

Ques 28.

Using the method of undetermined coefficients, solve the differential equation:

$$(D^3 + 2D^2 - D - 2)y = e^x + x^2.$

Ques 29.

Solve the differential equation: $\frac{dy}{dx} = (x + y)^2$ .

Ques 30.

Solve the differential equation: $\frac{dy}{dx} = (x + y)^2$ . A particle falls from rest in a medium in which the resistance is $\lambda v^2$ per unit mass, v being the velocity of the particle at time t. Prove that the distance fallen in time t is $\frac{1}{\lambda} \ln \cosh (t\sqrt{g\lambda})$ , where g is the acceleration due to gravity.

Ques 31.

Solve: $(y^2 + yz)dx + (z^2 + zx)dy + (x^2 + xy)dz = 0$ .

Ques 32.

Solve: $(D^2 + 5DD' + 5D'^2)z = x \sin (3x - 2y)$ .

Ques 33.

Solve: $\frac{dx}{y^2 + yz + z^2} = \frac{dy}{z^2 + zx + x^2} = \frac{dz}{x^2 + xy + y^2}$ .

Ques 34.

Using the method of variation of parameters, solve the equation

$$\frac{d^2y}{dx^2} + a^2y = \sec ax.$

Ques 35.

Solve $(p + q)(px + qy) = 1$ , using Charpit's method.

Ques 36.

Solve: $\frac{dy}{dx} = \frac{1}{x + y + 1}$ .

Ques 37.

Solve: $(D^2 - DD' - 2D) z = \sin(3x + 4y) + e^{2x+y}$ .

Ques 38.

Use the method of variation of parameters to solve the following differential equation:

$$y'' - 2y' + y = \frac{12e^x}{x^3}.$

Ques 39.

Solve: $x^2y'' - 2xy' - 4y = x^2 + 2\ln x$ .

Ques 40.

) Solve the equation $(7y - 3x + 3)dy + (3y - 7x + 7)dx = 0$ .

Ques 41.

Using the method of undetermined coefficients, solve the equation

$$\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + 2y = 4x^2.$

Ques 42.

Using Charpit's method, solve the equation

$$zp^2 - y^2p + y^2q = 0.$

Ques 43.

Ques 44.

अवकल समीकरण :

$$y'' + 6y' + 9y = \frac{1}{x^3}e^{-3x}, \text{ x} > 0.$ $
को प्राचल विचरण विधि से हल कीजिए।

Ques 45.

Ques 46.

Ques 47.

हल कीजिए : $(x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0$ . $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(5)$

Ques 48.

हल कीजिए : $(x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0$ . $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(5)$

Ques 49.

अनिर्धारित गुणांक विधि से अवकल समीकरण :
$$(D^3 + 2D^2 - D - 2)y = e^x + x^2.$ $
को हल कीजिए। (4)

Ques 50.

अवकल समीकरण $\frac{dy}{dx} = (x + y)^2$ को हल कीजिए।

Ques 51.

Ques 52.

हल कीजिए : $(y^2 + yz)dx + (z^2 + zx)dy + (y^2 - xy)dz = 0.$

Ques 53.

हल कीजिए : $(D^2 + 5DD' + 5D'^2)z = x \sin (3x - 2y).$

Ques 54.

) हल कीजिए : $\frac{dx}{y^2 + yz + z^2} = \frac{dy}{z^2 + zx + x^2} = \frac{dz}{x^2 + xy + y^2}.$

Ques 55.

Ques 56.

चार्पिट विधि द्वारा समीकरण $(p + q)(px + qy) = 1$ का हल प्राप्त कीजिए। $\quad\quad\quad\quad\quad$

Ques 57.

हल कीजिए : $\frac{dy}{dx} = \frac{1}{x + y + 1}.$ $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$ (2)

Ques 58.

हल कीजिए : $(D^2 - DD' - 2D) z = \sin(3x + 4y) + e^{2x+y}.$ $\quad\quad\quad\quad\quad\quad\quad\quad$

Ques 59.

Ques 60.

$6xy \, dx + (4y + 9x^2) \, dy = 0$ .

Ques 61.

The solution of the differential equation $\frac{dy}{d} = y$ with $y(0) = 0$ exists, but is not unique.

Ques 62.

$\sin x \frac{d^2y}{dx^2} + \frac{dy}{dx} + y = 0$ in $]0, \pi[$ is a linear homogeneous equation

Ques 63.

The solution of the differential equation

$\frac{dy}{dx} = y$ with $y(0) = 0$

exists, but is not unique.

Ques 64.

The Pfaffian equation $(2xy^2 + 2xy + 2xz^2 + 1)dx + dy + 2z \, dz = 0$ is integrable.

Ques 65.

Apply the method of variation of parameter to solve the differential equation:

$$y'' + 6y' + 9y = \frac{1}{x^3} e^{-3x}, \quad x > 0.$

Ques 66.

Ques 67.

Find the integral surface of the p.d.e.:

$$(x - y)p + (y - x - z)q = z$

through the circle $z = 1, x^2 + y^2 = 1$ .

Ques 68.

Solve: $(x^2y - 2xy^2)dx - (x^3 - 3x^2y)dy = 0$ .

Ques 69.

Using Charpit's method, find the complete integral of the p.d.e.:

$$2xz - px^2 - 2qxy + pq = 0.$

Ques 70.

Using the method of undetermined coefficients, solve the differential equation:

$$(D^3 + 2D^2 - D - 2)y = e^x + x^2.$

Ques 71.

Solve the differential equation: $\frac{dy}{dx} = (x + y)^2$ .

Ques 72.

Ques 73.

Solve: $(y^2 + yz)dx + (z^2 + zx)dy + (x^2 + xy)dz = 0$ .

Ques 74.

Solve: $(D^2 + 5DD' + 5D'^2)z = x \sin (3x - 2y)$ .

Ques 75.

Solve: $\frac{dx}{y^2 + yz + z^2} = \frac{dy}{z^2 + zx + x^2} = \frac{dz}{x^2 + xy + y^2}$ .

Ques 76.

Using the method of variation of parameters, solve the equation

$$\frac{d^2y}{dx^2} + a^2y = \sec ax.$

Ques 77.

Solve $(p + q)(px + qy) = 1$ , using Charpit's method.

Ques 78.

Solve: $\frac{dy}{dx} = \frac{1}{x + y + 1}$ .

Ques 79.

Solve: $(D^2 - DD' - 2D) z = \sin(3x + 4y) + e^{2x+y}$ .

Ques 80.

Use the method of variation of parameters to solve the following differential equation:

$$y'' - 2y' + y = \frac{12e^x}{x^3}.$

Ques 81.

Solve: $x^2y'' - 2xy' - 4y = x^2 + 2\ln x$ .

Ques 82.

) Solve the equation $(7y - 3x + 3)dy + (3y - 7x + 7)dx = 0$ .

Ques 83.

Using the method of undetermined coefficients, solve the equation

$$\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + 2y = 4x^2.$

Ques 84.

Using Charpit's method, solve the equation

$$zp^2 - y^2p + y^2q = 0.$

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Course Name	Bachelor of Science
Course Code	BSCG
Programm	BACHELOR DEGREE PROGRAMMES Courses
Language	English

IGNOU BMTC 132 Solved Assignment

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IGNOU BMTC 132 SOLVED ASSIGNMENT HINDI

IGNOU BMTC 132 SOLVED ASSIGNMENT HINDI

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