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This mock test of Differential Equations - 4 for Mathematics helps you for every Mathematics entrance exam.
This contains 20 Multiple Choice Questions for Mathematics Differential Equations - 4 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Let a, b ∈ R. Let y = (y_{1}, y_{2})^{T} be a solution of the system of equations

Every solution y(x) → 0 as x → ∞ if

Solution:

QUESTION: 2

The solution of exists for all

Solution:

QUESTION: 3

For solving by variation of parameters. The value of Wronskion W is

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QUESTION: 4

The initial value problem

Solution:

QUESTION: 5

Consider the following statements

I. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.

II. If T(x, y) = 0 is the equation of the tac-locus, then

T(x, y ) is a factor of the P-discriminant.

III. T(x, y ) is a factor of a c-discriminant.

IV. Cusp-locus has two distinct tangent.

Choose the correct answer.

Solution:

QUESTION: 6

The general solution

where andy(0) = 0 is

Solution:

QUESTION: 7

Which of the following pair of function are linear independent

Select the correct code

Solution:

QUESTION: 8

Singular solution of differential equation contains

I. arbitrary constant

II. can be obtained from general

III. do not contain arbitrary constant

IV. cannot be obtained from general solution

Solution:

QUESTION: 9

For non-homogeneous equation y' + p(x)y = r(x), if y_{1} and y_{2} are its solutions, then the solution of homogeneous equation y' + p(x)y = 0 is

Solution:

QUESTION: 10

The solution of represents

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QUESTION: 11

Solve for 0 < y < 10 and y (0) = 0

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QUESTION: 12

The orthogonal trajectory of the family x^{2} - y^{2} = C_{2} are given by

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QUESTION: 13

A. Singular solution contains no arbitrary constants.

B. Singular solution can be obtained from complete primitive.

Solution:

QUESTION: 14

The solution of the differential equation sin x = 0, y(0) = 0 exists in the open interval (-a, a) then ‘a’ equals to

Solution:

QUESTION: 15

If y_{1}(x) = x and y_{2}(x) = xe^{x} are two linearly independent solutions of then the interval on which they form a fundam ental set of solution is

Solution:

QUESTION: 16

Using the method of variation of parameters for the particular solution to the differential equation

Solution:

QUESTION: 17

The general solution of the system of differential equation and M a 2 x 2 matrix and a 2 x 1 constant vector b = is given by

Solution:

QUESTION: 18

For the ordinary differential equation

which of the following statement is true?

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QUESTION: 19

If 2x(1 - y ) = K and g(x, y) = L are orthogonal families of curves where K and L constants, then g(x, y) is

Solution:

QUESTION: 20

If y_{1 }and y_{2} are linearly independent solutions of the homogeneous equation L(y) =y"+p_{1}(x)y' + p_{2}(x)y = 0. Then, p_{1}(x) and p_{2}{x) are given by

Solution:

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