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This mock test of Differential Equation MCQ Level - 1 for Physics helps you for every Physics entrance exam.
This contains 10 Multiple Choice Questions for Physics Differential Equation MCQ Level - 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The integrating factor of the differential equation, would be :

Solution:

The given differential equation is homogeneous

Consider,

Comparing it with the equation

We have,

Also, the equation is homogeneous &

∴ The integrating factor would be given by

The correct answer is: *x*

QUESTION: 2

The curve r = a(secθ + tanθ) is orthogonal to :

Solution:

Given,

Replacing to get the orthogonal curve,

Integrating both sides

The correct answer is:

QUESTION: 3

Solution to the differential equation

Solution:

which is a linear equation

The required solution will be given by

The correct answer is:

5*y* = *x*^{4} + *ax*^{–1}

QUESTION: 4

What would be the order and degree of the given differential equation

Solution:

Consider the differential equation,

Cubing both sides,

∴ according to definition, degree of the above differential equation is 3 and order is 2.

The correct answer is: Order–2 & Degree–3

QUESTION: 5

The general solution of the differential equation, will be given by.

Solution:

We have

Putting the above equations becomes

Auxiliary equation :

Hence,

The correct answer is:

QUESTION: 6

The general solution of the differential equation,

will be given by :

Solution:

Since ** y = e^{x}** is an integral, we take

^{}

The given equation becomes

Hence ** y = ve^{x} = (c_{1} log x + c_{2})e^{x}** is the complete solution.

The correct answer is: (*C*_{1} log *x* + *C*_{2})*e ^{x}*

QUESTION: 7

The particular integral of the differential equation,

will be

Solution:

Multiplying the given equation by ** x^{2}** we obtain

Then the equation, on putting becomes

The correct answer is:

QUESTION: 8

The solution of

Solution:

Comparing it with the equation,

*Mdx* + *Ndy* = 0

We have,

* M* = *y* cos *x* + sin *y* + *y* & *N* = sin *x* + *x* cos *y* + *x
*

Hence, the given differential equation is exact.

∴ The required solution will be given by,

The correct answer is: *y* sin *x* + (sin *y* + *y*) *x* = *c*

QUESTION: 9

The differential equation, can be reduced into which of the following linear equation?

Solution:

We have ** P + Qx = –x^{2} + x^{2} = 0** and so

Let ** y = vx** so that

Now the given equation reduces to

QUESTION: 10

Which of the following function form the solution of the differential equation, [x^{2}D^{2} – xD + 2]y = log x?

Solution:

On putting the given equation becomes

The auxiliary equation is

Hence, is the solution:

The correct answer is:

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