Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.

1.

Particular solution of the differential equation ( frac{dy}{dx} = frac{x+y}{x}:y(1)=1 ) is _____

A. x =y log|x| + y
B. y = y log|x| + 2x
C. x = x log|y| + y
D. y = x log|x| + x
Answer» E.
Discussion
2.

Solution of the differential equation ( Big[ frac{e^{-2 sqrt{x}}}{ sqrt{x}} frac{y}{ sqrt{x}} Big] frac{dy}{dx} = 1, ,x 0 ) is _______

A. (ye^{2 sqrt{x}}=2 sqrt{x}+c )
B. (ye^{-2 sqrt{x}}=2x^{- frac{3}{2}}+c )
C. (ye^{-2 sqrt{x}}=3 sqrt{x}+c )
D. (ye^{2 sqrt{x}}=3x^{ frac{3}{2}}+c )
Answer» B. (ye^{-2 sqrt{x}}=2x^{- frac{3}{2}}+c )
Discussion
3.

Solution of the differential equation ((x+3y^2) frac{dy}{dx} = y(y>0) ) is ______________

A. x=3y<sup>2</sup>+cy
B. y=2x<sup>2</sup>+c
C. x=2y<sup>2</sup>+ ( frac{c}{y} )
D. y=3x<sup>3</sup>+c
Answer» B. y=2x<sup>2</sup>+c
Discussion
4.

For the differential equation ( frac{dy}{dx} ) 3y cot x = sin 2x; y=2 when x= ( frac{ pi}{2} ), its particular solution is ______

A. y = 2cos<sup>2</sup> x + 4cos<sup>3</sup> x
B. y = -2sin<sup>3</sup> x + 4sin<sup>2</sup> x
C. y = -2sin<sup>2</sup> x + 4sin<sup>3</sup> x
D. y = 4cos<sup>2</sup> x + 2sin<sup>3</sup> x
Answer» D. y = 4cos<sup>2</sup> x + 2sin<sup>3</sup> x
Discussion
5.

Solution of the differential equation ( frac{dy}{dx} ) + y cot x = cos x is ______

A. (y cos ,x = frac{sin^2 x}{2} + c )
B. (y sin ,x = frac{sin^2 x}{2} + c )
C. (y sin ,x = frac{cos^2 x}{4} + c )
D. (y cos ,x = - frac{sin^2 x}{4} + c )
Answer» C. (y sin ,x = frac{cos^2 x}{4} + c )
Discussion