Differential Equations - 4


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Differential Equations - 4

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Differential Equations - 4 - Question 1

Let a, b ∈ R. Let y = (y1, y2)T be a solution of the system of equations

Every solution y(x) → 0 as x → ∞ if

Differential Equations - 4 - Question 2

The solution of  exists for all 

Differential Equations - 4 - Question 3

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

Differential Equations - 4 - Question 4

The initial value problem

Differential Equations - 4 - 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.

Differential Equations - 4 - Question 6

The general solution 
where  andy(0) = 0 is

Differential Equations - 4 - Question 7

Which of the following pair of function are linear independent




Select the correct code

Differential Equations - 4 - 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

Differential Equations - 4 - Question 9

For non-homogeneous equation y' + p(x)y = r(x), if y1 and y2 are its solutions, then the solution of homogeneous equation y' + p(x)y = 0 is

Differential Equations - 4 - Question 10

The solution of  represents

Differential Equations - 4 - Question 11

Consider the differential equation (x + y + 1) dx + (2x + 2y + 1)dy = 0. Which of the following statement is true? 

Detailed Solution for Differential Equations - 4 - Question 11

Here (x + y + 1)dx + (2x + 2y + 1)dy = 0




By separables of variables,

Integrating (2z + log z) = x + c
⇒ 2(x + y) + log (x + y) = x + c.

Differential Equations - 4 - Question 12

The orthogonal trajectory of the family x2 - y2 = C2 are given by

Differential Equations - 4 - Question 13

A. Singular solution contains no arbitrary constants.
B. Singular solution can be obtained from complete primitive.

Differential Equations - 4 - Question 14

Let the general solution of a differential equation be, y = aebx+c then order of the differential equation is,

Differential Equations - 4 - Question 15

If y1(x) = x and y2(x) = xex are two linearly independent solutions of  then the interval on which they form a fundam ental set of solution is

Differential Equations - 4 - Question 16

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

Differential Equations - 4 - 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

Differential Equations - 4 - Question 18

For the ordinary differential equation

which of the following statement is true?

Differential Equations - 4 - 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

Differential Equations - 4 - Question 20

If yand y2 are linearly independent solutions of the homogeneous equation L(y) =y"+p1(x)y' + p2(x)y = 0. Then, p1(x) and p2{x) are given by

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