IGNOU PHE 5 SOLVED ASSIGNMENT HINDI

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IGNOU PHE 5 SOLVED ASSIGNMENT HINDI

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IGNOU PHE 5 SOLVED ASSIGNMENT HINDI

~~Rs. 80~~
Rs. 41

Last Date of Submission of IGNOU PHE-05 (BSC) 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 PHE 5 SOLVED ASSIGNMENT HINDI
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSC
Course Name	Bachelor in Science
Subject Code	PHE 5
Subject Name	Mathematical Methods in Physics-II
Year	2026
Session
Language	English Medium
Assignment Code	PHE-05/Assignmentt-1//2026
Product Description	Assignment of BSC (Bachelor in Science) 2026. Latest PHE 05 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU PHE-05 (BSC) 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.

निम्नलिखित साधारण अवकल समीकरणों को हल करें :

(i) $x dx + y dy + 4y^3(x^2 + y^2) dy = 0$

(ii) $y'' + 4y = 2 \cos x \cos 3x$

Ques 2.

निम्नलिखित आदि मान समस्या को हल करें :

$\frac{d^2x}{dt^2} - 3 \frac{dx}{dt} - 10x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0$

Ques 3.

एक आदमी पैराशूट के साथ गिर रहा है। जब उसका पैराशूट खुलता है, उसकी चाल $50 \text{ ms}^{-1}$ है। यदि वायु प्रतिरोध (Mv²)/25 है, जहां M आदमी और पैराशूट का द्रव्यमान है, पैराशूट खुलने के बाद आदमी के चाल को समय t के फलन के रूप में प्राप्त करें। $g = 10 \text{ ms}^{-1}$ लें। (10) (नोट: छवि में g की इकाई $\text{ms}^{-1}$ लिखी है, जो संभवतः $\text{ms}^{-2}$ होनी चाहिए)

Ques 4.

$1.0 \text{ m}$ व्यास वाला एक बेलन पानी में ऐसे खड़ा है कि उसका अक्ष ऊर्ध्वाधर दिशा में है। जब उसे थोड़ा सा दबाकर छोड़ दिया जाता है, वह $2 \text{ s}$ की आवर्तकाल के साथ दोलन करता है। बेलन का द्रव्यमान प्राप्त करें।

Ques 5.

फोबेनियस विधि द्वारा निम्नलिखित साधारण अवकल समीकरण का हल प्राप्त करें :

$\frac{d^2y}{dx^2} + \frac{1}{2x} \frac{dy}{dx} + y = 0$

Ques 6.

दिखायें कि फलन

$$u = e^{-\omega^2 c^2 t} \sin(\omega x)$

एक-विमिय ताप समीकरण का हल है।

Ques 7.

निम्नलिखित फलन के सभी प्रथम और द्वितीय कोटि के आंशिक अवकलज प्राप्त करें :

$$u(x, y) = x^2 \sin y + y^2 \cos x$

Ques 8.

त्रिज्या A वाली एक गेंद की सतह को शून्य तापमान पर रखा जाता है। यदि गेंद में आदि तापमान f(r) है तो परिसीमा प्रतिबन्ध लिखें और दिखाएं कि समय t पर गेंद में तापमान u(r, t), निम्नलिखित समीकरण का हल है:

$$c^2 \left( \frac{\partial^2 u}{\partial r^2} + \frac{2}{r} \frac{\partial u}{\partial r} \right) = \frac{\partial u}{\partial t}$

Ques 9.

$2\pi$ आवर्तकाल वाले निम्नलिखित आवर्ती फलन का फूरिए श्रेणी प्रसार प्राप्त करें :

$f(x) = \pi^2 - x^2, -\pi < x < 0$ के लिए।

Ques 10.

लंबाई L वाले एक कम्पमान तार के दोनों सिरे स्थिर हैं। तार का आदि वेग शून्य है तथा आदि विक्षेपण निम्नलिखित फलन द्वारा परिभाषित है :

$$f(x) = Ax \qquad\qquad\qquad 0 \le x \le L/4$
$$\quad\;\;\; = AL/4 \qquad\qquad\quad L/4 \le x \le 3L/4$
$$\quad\;\;\; = A(L - x) \qquad\quad 3L/4 \le x \le L$

इन प्रतिबन्धों के लिए तार का विक्षेपण u(x, t) प्राप्त करें।

Ques 11.

Solve the following ordinary differential equations:

(i) $x dx + y dy + 4y^3(x^2 + y^2)dy = 0$

(ii) $y'' + 4y = 2 \cos x \cos 3x$

Ques 12.

Solve the initial value problem:

$\frac{d^2x}{dt^2} - 3\frac{dx}{dt} - 10x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0$

Ques 13.

A parachutist is falling with a speed of $50 \text{ ms}^{-1}$ when his parachute opens. If the air resistance is (Mv²)/25 where M is the total mass of the man and his parachute, find the speed of the man as a function of time t after the parachute opens. Take $g = 10 \text{ ms}^{-1}$ .

Ques 14.

A cylinder with a diameter $1.0 \text{ m}$ is stands in water with its axis vertical. When depressed slightly and released, it oscillates with a time period of $2 \text{ s}$ . Determine the mass of the cylinder.

Ques 15.

Solve the following ODE using the Frobenius method:

$\frac{d^2y}{dx^2} + \frac{1}{2x} \frac{dy}{dx} + y = 0$

Ques 16.

Show that:

$$u = e^{-\omega^2 c^2 t} \sin(\omega x)$
is a solution of the one-dimensional heat equation.

Ques 17.

Determine all the first and second order partial derivatives for the function:

$$u(x, y) = x^2 \sin y + y^2 \cos x$

Ques 18.

The surface of a ball of radius A is kept at a temperature zero. If the initial temperature in the ball is f(r), write down the boundary conditions and show that the temperature in the ball at time t, u(r, t), is the solution to the equation:

$$c^2 \left( \frac{\partial^2 u}{\partial r^2} + \frac{2}{r} \frac{\partial u}{\partial r} \right) = \frac{\partial u}{\partial t}$

Ques 19.

Obtain the Fourier series for the following periodic function which has a period of $2\pi$ :

$$f(x) = \pi^2 - x^2 \text{ for } -\pi < x < \pi$

Ques 20.

Determine the deflection u(x, t) of a vibrating string of length L, which has its ends fixed, corresponding to a zero initial velocity and an initial deflection given by the function:

$$f(x) = \begin{cases} Ax & 0 \le x \le L/4 \\ AL/4 & L/4 \le x \le 3L/4 \\ A(L - x) & 3L/4 \le x \le L \end{cases}$

Ques 21.

निम्नलिखित साधारण अवकल समीकरणों को हल करें :

(i) $x dx + y dy + 4y^3(x^2 + y^2) dy = 0$

(ii) $y'' + 4y = 2 \cos x \cos 3x$

Ques 22.

निम्नलिखित आदि मान समस्या को हल करें :

$\frac{d^2x}{dt^2} - 3 \frac{dx}{dt} - 10x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0$

Ques 23.

Ques 24.

Ques 25.

फोबेनियस विधि द्वारा निम्नलिखित साधारण अवकल समीकरण का हल प्राप्त करें :

$\frac{d^2y}{dx^2} + \frac{1}{2x} \frac{dy}{dx} + y = 0$

Ques 26.

दिखायें कि फलन

$$u = e^{-\omega^2 c^2 t} \sin(\omega x)$

एक-विमिय ताप समीकरण का हल है।

Ques 27.

निम्नलिखित फलन के सभी प्रथम और द्वितीय कोटि के आंशिक अवकलज प्राप्त करें :

$$u(x, y) = x^2 \sin y + y^2 \cos x$

Ques 28.

$$c^2 \left( \frac{\partial^2 u}{\partial r^2} + \frac{2}{r} \frac{\partial u}{\partial r} \right) = \frac{\partial u}{\partial t}$

Ques 29.

$f(x) = \pi^2 - x^2, -\pi < x < 0$ के लिए।

Ques 30.

$$f(x) = Ax \qquad\qquad\qquad 0 \le x \le L/4$
$$\quad\;\;\; = AL/4 \qquad\qquad\quad L/4 \le x \le 3L/4$
$$\quad\;\;\; = A(L - x) \qquad\quad 3L/4 \le x \le L$

इन प्रतिबन्धों के लिए तार का विक्षेपण u(x, t) प्राप्त करें।

Ques 31.

Solve the following ordinary differential equations:

(i) $x dx + y dy + 4y^3(x^2 + y^2)dy = 0$

(ii) $y'' + 4y = 2 \cos x \cos 3x$

Ques 32.

Solve the initial value problem:

$\frac{d^2x}{dt^2} - 3\frac{dx}{dt} - 10x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0$

Ques 33.

Ques 34.

Ques 35.

Solve the following ODE using the Frobenius method:

$\frac{d^2y}{dx^2} + \frac{1}{2x} \frac{dy}{dx} + y = 0$

Ques 36.

Show that:

$$u = e^{-\omega^2 c^2 t} \sin(\omega x)$
is a solution of the one-dimensional heat equation.

Ques 37.

Determine all the first and second order partial derivatives for the function:

$$u(x, y) = x^2 \sin y + y^2 \cos x$

Ques 38.

$$c^2 \left( \frac{\partial^2 u}{\partial r^2} + \frac{2}{r} \frac{\partial u}{\partial r} \right) = \frac{\partial u}{\partial t}$

Ques 39.

Obtain the Fourier series for the following periodic function which has a period of $2\pi$ :

$$f(x) = \pi^2 - x^2 \text{ for } -\pi < x < \pi$

Ques 40.

Determine the deflection u(x, t) of a vibrating string of length L, which has its ends fixed, corresponding to a zero initial velocity and an initial deflection given by the function:

$$f(x) = \begin{cases} Ax & 0 \le x \le L/4 \\ AL/4 & L/4 \le x \le 3L/4 \\ A(L - x) & 3L/4 \le x \le L \end{cases}$

~~Rs. 80~~
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Course Name	Bachelor in Science
Course Code	BSC
Programm	BACHELOR DEGREE PROGRAMMES Courses
Language	English

IGNOU PHE 5 Solved Assignment

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IGNOU PHE 5 SOLVED ASSIGNMENT HINDI

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