IGNOU BMTC 132 SOLVED ASSIGNMENT 2025

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IGNOU BMTC 132 SOLVED ASSIGNMENT 2025

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IGNOU BMTC 132 Solved Assignment 2025

This is latest Solved Assignment of BMTC 132 of BAG .

Latest 2025 Solved Assignment
Fully Solved BMTC 132 2025 Assignment
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BMTC 132 ( Differential Equations )
Differential Equations 2025 Solved Assignment
2025 New Assignment

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Last Date of Submission of IGNOU BMTC-132 (BAG) 2025 Assignment is for January 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Semester Wise
January 2025 Session: 30th March, 2025 (for June 2025 Term End Exam).
July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).

Title Name	IGNOU BMTC 132 Solved Assignment 2025
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BAG
Course Name	BACHELOR OF ARTS
Subject Code	BMTC 132
Subject Name	Differential Equations
Year	2025
Session
Language	English Medium
Assignment Code	BMTC-132/Assignmentt-1//2025
Product Description	Assignment of BAG (BACHELOR OF ARTS) 2025. Latest BMTC 132 2025 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BMTC-132 (BAG) 2025 Assignment is for January 2025 Session: 30th September, 2025 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2025 (for June 2025 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).

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Questions Included in this Help Book

Ques 1.

Solve the differential equations:

$\frac{dy}{dx}=-\frac{2x+y+1}{4x+2y-1}$

Ques 2.

Solve the simultaneous equations:

$\frac{dx}{y-z}=\frac{dy}{z-x}=\frac{dz}{x-y}$

Ques 3.

By using the method of variation of parameter, find the general solution of the differential equation:

$y''+y=\sec^2 x$

Ques 4.

If:

Z= x²y+2xy²

where x = sin zt

and

y = cost

find dz/dt when t=0by (i) chain rule and by (ii) the direct substitution.

Ques 5.

Verify that the differential equation:

z(x²-y²-z^²)dx+(x+z)xzdy

+ x(z²-x2-xy)dz = 0

is integrable and find its integral.

Ques 6.

Solve:

$y'=\frac{zy^4+x^4}{xy^3}$

Ques 7.

Find the general solution of the equation:

x(y²-z²)u_x + y(z²-x²)u_y +z(x²- y²)u₂ = 0

Ques 8.

Show that for the function f given by:

$f(x,y)=\frac{xy}{x^2+y^2}$

$\lim_{x\rightarrow0}\lim_{y\rightarrow0}f(x,y)=\lim_{y\rightarrow0}\lim_{x\rightarrow0}f(x,y)=0$

$\text{But}\lim_{(x,y)\rightarrow(0,0)}f(x,y)\text{does not exist.}$

Ques 9.

Show that the following function f is differentiable at (0,0):

$f(x,y)=\begin{cases}\frac{x^2 y^2}{x^2+y^2},&\text{if}(x,y)\ne(0,0)\\0,&\text{if}(x,y)=(0,0)\end{cases}$

Ques 10.

Find the complete solution of the equation px + qy = pq.

Ques 11.

Using Charpit’s method, find the complete integral of the differential equation:

p²x + q²y = z

Ques 12.

Find partial derivatives f_x and f_y for the function:

f(x,y) = 5x⁴y² + 6x²y³

at the point ,(1,-1)

Ques 13.

State Euler’s theorem for homogeneous functions and verify it for the function:

$u=\frac{x^3+y^3}{x+y}$

Ques 14.

The population of a town grows at a rate proportional to the population at any time. Its initial population of 500 increases by 15% in 10 years. What will be the population in 30 years?

Ques 15.

Show that the following function is not continuous at (0,0):

$f(x,y)=\begin{cases}y\sin{\frac{1}{x}}+x\sin{\frac{1}{y}},&x\ne 0,y\ne 0\\1,&\text{otherwise}\end{cases}$

Ques 16.

अवकल समीकरण :

$\frac{dy}{dx}=-\frac{2x+y+1}{4x+2y-1}$

का हल प्राप्त कीजिए।

Ques 17.

युगपत समीकरणों :

$\frac{dx}{y-z}=\frac{dy}{z-x}=\frac{dz}{x-y}$

का हल प्राप्त कीजिए।

Ques 18.

प्राचल विचार विधि से अवकल समीकरण :

y" + y = sec² x

का व्यापक हल प्राप्त कीजिए।

Ques 19.

यदि :

Z=x²y+2xy⁴

जहाँ x = sin zt

और y = cost

तो dz/dt ज्ञात कीजिए: (i) श्रृंखला नियम और (ii) प्रत्यक्ष प्रतिस्थापन से जहां t = 0 |

Ques 20.

सत्यापित कीजिए कि अवकल समीकरण :

z(x²-y²-z^²)dx+(x+z)xzdy +x(z²-x²-xy)dz = 0

समाकलनीय है और इसका समाकल भी ज्ञात कीजिए।

Ques 21.

हल कीजिए :

y'=zy^$+x 4 / xy³

Ques 22.

समीकरण :

x(y²-z²)ux + y(z² -x²)u, +z(x²-y²)u_₂ = 0

का व्यापक हल प्राप्त कीजिए।

Ques 23.

$f(x,y)=\frac{xy}{x^2+y^2}$ द्वारा दिए गए फलन के लिए दिखाइए कि :

लेकिन का अस्तित्व नहीं होता।

Ques 24.

दिखाइए कि निम्नलिखित फलन f, (0,0) पर अवकलनीय है :

$f(x,y)=\begin{cases}\frac{x^2 y^2}{x^2+y^2},&\text{if}(x,y)\ne(0,0)\\0,&\text{if}(x,y)=(0,0)\end{cases}$

Ques 25.

समीकरण px+qy = pq का पूर्ण हल प्राप्त कीजिए।

Ques 26.

चारपिट विधि का उपयोग करते हुए, अवकल समीकरण p²x+q²y = z का पूर्ण समाकल ज्ञात कीजिए।

Ques 27.

बिन्दु (1,-1) पर फलन f(x,y) = 5x⁴+y² +6x²y³ के लिए, आंशिक अवकलज f_x और f_y ज्ञात कीजिए।

Ques 28.

समघात फलनों के लिए, ऑयलर प्रमेय का कथन लिखिए तथा फलन $u=\frac{x^3+y^3}{x+y}$ के लिए उसका सत्यापन कीजिए।

Ques 29.

एक शहर की जनसंख्या में किसी (उस) समय की जनसंख्या के समानुपात की दर पर वृद्धि होती है। उसकी प्रारम्भिक जनसंख्या 500 में 10 वर्षों में 15% वृद्धि हो जाती है। 30 वर्षों में यह जनसंख्या कितनी हो जाएगी?

Ques 30.

दर्शनीय कि फलन :

$f(x,y)=\begin{cases}y\sin\frac{1}{x}+x\sin\frac{1}{y},&x\ne 0,y\ne 0\\1,\end{cases}$ अन्यथा

बिन्दु (0,0) पर संतत नहीं है।

Ques 31.

Solve the differential equations:

$\frac{dy}{dx}=-\frac{2x+y+1}{4x+2y-1}$

Ques 32.

Solve the simultaneous equations:

$\frac{dx}{y-z}=\frac{dy}{z-x}=\frac{dz}{x-y}$

Ques 33.

By using the method of variation of parameter, find the general solution of the differential equation:

$y''+y=\sec^2 x$

Ques 34.

By using the method of variation of parameter, find the general solution of the differential equation:

$y''+y=\sec^2 x$

Ques 35.

If:

Z= x²y+2xy²

where x = sin zt

and

y = cost

find dz/dt when t=0by (i) chain rule and by (ii) the direct substitution.

Ques 36.

Verify that the differential equation:

z(x²-y²-z^²)dx+(x+z)xzdy

+ x(z²-x2-xy)dz = 0

is integrable and find its integral.

Ques 37.

Verify that the differential equation:

z(x²-y²-z^²)dx+(x+z)xzdy

+ x(z²-x2-xy)dz = 0

is integrable and find its integral.

Ques 38.

Solve:

$y'=\frac{zy^4+x^4}{xy^3}$

Ques 39.

Find the general solution of the equation:

x(y²-z²)u_x + y(z²-x²)u_y +z(x²- y²)u₂ = 0

Ques 40.

Show that for the function f given by:

$f(x,y)=\frac{xy}{x^2+y^2}$

$\lim_{x\rightarrow0}\lim_{y\rightarrow0}f(x,y)=\lim_{y\rightarrow0}\lim_{x\rightarrow0}f(x,y)=0$

$\text{But}\lim_{(x,y)\rightarrow(0,0)}f(x,y)\text{does not exist.}$

Ques 41.

Solve the differential equations:

$\frac{dy}{dx}=-\frac{2x+y+1}{4x+2y-1}$

Ques 42.

Solve the simultaneous equations:

$\frac{dx}{y-z}=\frac{dy}{z-x}=\frac{dz}{x-y}$

Ques 43.

By using the method of variation of parameter, find the general solution of the differential equation:

$y''+y=\sec^2 x$

b) If:

Z= x²y+2xy²

where x = sin zt

and

y = cost

find dz/dt when t=0by (i) chain rule and by (ii) the direct substitution.

Ques 44.

Verify that the differential equation:

z(x²-y²-z^²)dx+(x+z)xzdy

+ x(z²-x2-xy)dz = 0

is integrable and find its integral.

Ques 45.

Solve:

$y'=\frac{zy^4+x^4}{xy^3}$

Ques 46.

Find the general solution of the equation:

x(y²-z²)u_x + y(z²-x²)u_y +z(x²- y²)u₂ = 0

Ques 47.

Show that for the function f given by:

$f(x,y)=\frac{xy}{x^2+y^2}$

$\lim_{x\rightarrow0}\lim_{y\rightarrow0}f(x,y)=\lim_{y\rightarrow0}\lim_{x\rightarrow0}f(x,y)=0$

$\text{But}\lim_{(x,y)\rightarrow(0,0)}f(x,y)\text{does not exist.}$

Ques 48.

Show that the following function f is differentiable at (0,0):

$f(x,y)=\begin{cases}\frac{x^2 y^2}{x^2+y^2},&\text{if}(x,y)\ne(0,0)\\0,&\text{if}(x,y)=(0,0)\end{cases}$

Ques 49.

Find the complete solution of the equation px + qy = pq.

Ques 50.

Using Charpit’s method, find the complete integral of the differential equation:

p²x + q²y = z

Ques 51.

Using Charpit’s method, find the complete integral of the differential equation:

p²x + q²y = z

Ques 52.

Find partial derivatives f_x and f_y for the function:

f(x,y) = 5x⁴y² + 6x²y³

at the point ,(1,-1)

Ques 53.

Find partial derivatives f_x and f_y for the function:

f(x,y) = 5x⁴y² + 6x²y³

at the point ,(1,-1)

Ques 54.

State Euler’s theorem for homogeneous functions and verify it for the function:

$u=\frac{x^3+y^3}{x+y}$

Ques 55.

The population of a town grows at a rate proportional to the population at any time. Its initial population of 500 increases by 15% in 10 years. What will be the population in 30 years?

Ques 56.

Show that the following function is not continuous at (0,0):

$f(x,y)=\begin{cases}y\sin{\frac{1}{x}}+x\sin{\frac{1}{y}},&x\ne 0,y\ne 0\\1,&\text{otherwise}\end{cases}$

Ques 57.

अवकल समीकरण :

$\frac{dy}{dx}=-\frac{2x+y+1}{4x+2y-1}$

का हल प्राप्त कीजिए।

Ques 58.

युगपत समीकरणों :

$\frac{dx}{y-z}=\frac{dy}{z-x}=\frac{dz}{x-y}$

का हल प्राप्त कीजिए।

Ques 59.

प्राचल विचार विधि से अवकल समीकरण :

y" + y = sec² x

का व्यापक हल प्राप्त कीजिए।

Ques 60.

यदि :

Z=x²y+2xy⁴

जहाँ x = sin zt

और y = cost

तो dz/dt ज्ञात कीजिए: (i) श्रृंखला नियम और (ii) प्रत्यक्ष प्रतिस्थापन से जहां t = 0 |

Ques 61.

सत्यापित कीजिए कि अवकल समीकरण :

z(x²-y²-z^²)dx+(x+z)xzdy +x(z²-x²-xy)dz = 0

Ques 62.

हल कीजिए :

y'=zy^$+x 4 / xy³

Ques 63.

समीकरण :

x(y²-z²)ux + y(z² -x²)u, +z(x²-y²)u_₂ = 0

Ques 64.

$f(x,y)=\frac{xy}{x^2+y^2}$ द्वारा दिए गए फलन के लिए दिखाइए कि :

लेकिन का अस्तित्व नहीं होता।

Ques 65.

दिखाइए कि निम्नलिखित फलन f, (0,0) पर अवकलनीय है :

$f(x,y)=\begin{cases}\frac{x^2 y^2}{x^2+y^2},&\text{if}(x,y)\ne(0,0)\\0,&\text{if}(x,y)=(0,0)\end{cases}$

Ques 66.

समीकरण px+qy = pq का पूर्ण हल प्राप्त कीजिए।

Ques 67.

चारपिट विधि का उपयोग करते हुए, अवकल समीकरण p²x+q²y = z का पूर्ण समाकल ज्ञात कीजिए।

Ques 68.

बिन्दु (1,-1) पर फलन f(x,y) = 5x⁴+y² +6x²y³ के लिए, आंशिक अवकलज f_x और f_y ज्ञात कीजिए।

Ques 69.

Ques 70.

Ques 71.

दर्शनीय कि फलन :

$f(x,y)=\begin{cases}y\sin\frac{1}{x}+x\sin\frac{1}{y},&x\ne 0,y\ne 0\\1,\end{cases}$ अन्यथा

बिन्दु (0,0) पर संतत नहीं है।

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Course Name	BACHELOR OF ARTS
Course Code	BAG
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IGNOU BMTC 132 Solved Assignment

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