Differential Equation NAT Level - 1 - Physics MCQ

# Differential Equation NAT Level - 1 - Physics MCQ

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## 10 Questions MCQ Test Topic wise Tests for IIT JAM Physics - Differential Equation NAT Level - 1

Differential Equation NAT Level - 1 for Physics 2024 is part of Topic wise Tests for IIT JAM Physics preparation. The Differential Equation NAT Level - 1 questions and answers have been prepared according to the Physics exam syllabus.The Differential Equation NAT Level - 1 MCQs are made for Physics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Differential Equation NAT Level - 1 below.
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Differential Equation NAT Level - 1 - Question 1

### If the Particular Integral (P.I.) of the differential equation (D3 + 1)y = cos2x. is given by y = 1/65 (cos 2x - β sin 2x). Find the value of β

Detailed Solution for Differential Equation NAT Level - 1 - Question 1

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Differential Equation NAT Level - 1 - Question 2

### I.F of differential equation (y2 + 2x2y)dx + (2x3 – xy)dy = 0 is of the form xαyβ. Then find value of α + β

Detailed Solution for Differential Equation NAT Level - 1 - Question 2

Now, suppose, xh yk is IF then,

At this is exact so,

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Differential Equation NAT Level - 1 - Question 3

### The IF for the Differential Equation (1 + xy)y + x (1 - xy)dy/dx = 0 is xαyβ. Then find the value of the α + β.

Detailed Solution for Differential Equation NAT Level - 1 - Question 3

Comparing this equation with

Since, it is a homogeneous differential equation of form

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Differential Equation NAT Level - 1 - Question 4

Find the value of f(0) where f(x) is the Particular Integral (P.I.) of the Differential equation (D2 –2D + 1)y = x sin x.

Detailed Solution for Differential Equation NAT Level - 1 - Question 4

Applying the formula, we get

∴

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Differential Equation NAT Level - 1 - Question 5

Solve  In the solution find the value of constant which is in multiplication with cos x only given y(0) = 0.

Detailed Solution for Differential Equation NAT Level - 1 - Question 5

Auxiliary Equation is
m– 4m3 + 8m2 – 8m + 4 = 0
(m2 – 2m + 2)2 = 0
∴  m = 1 ± i, 1 ± i
Hence, sol of equation is

y =

Now,    y = 0 at x = 0
⇒  c1 = 0
Required constant c1 = 0.

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Differential Equation NAT Level - 1 - Question 6

Let y be a function of x satisfying dy/dx = 2x3  y(0) = 0, then find the value of e2y(1).

Detailed Solution for Differential Equation NAT Level - 1 - Question 6

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Differential Equation NAT Level - 1 - Question 7

Given a differential equation y(0) = 1, y(1) = e4, then y(4) = eα . Find the value of α.

Detailed Solution for Differential Equation NAT Level - 1 - Question 7

∴  Equation becomes

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Differential Equation NAT Level - 1 - Question 8

The Particular Integral (PI) of the differential equation (D2 – 5D + 6)y = x is given as y = mx + c. Find the value of c.

Detailed Solution for Differential Equation NAT Level - 1 - Question 8

y = mx + c
⇒ c = 5/36 = 0.138

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Differential Equation NAT Level - 1 - Question 9

If the differential equation (3a2y2x2 + bycosx)dx + (2sinx – 4ayx3)dy = 0 is exact then what is the value of   a, b ≠ 0.

Detailed Solution for Differential Equation NAT Level - 1 - Question 9

For Differential equation to be exact

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Differential Equation NAT Level - 1 - Question 10

If the Particular Integral (PI) of the Differential equation (D2 + a2)y = cos ax is given by f(x). Then find the value of a2f (π/2a).

Detailed Solution for Differential Equation NAT Level - 1 - Question 10

As, we known, the P.I. of (D2 + a2)y = cos ax is given as  x/2a sin ax
∴

Now,

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