Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 8 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{y^2-2xy-x^2}{y^2+2xy-x^2} ) given y=-1 at x=1.

A. y=x
B. y+x=2
C. y=-x
D. y-x=2
Answer» D. y-x=2
Discussion
2.

The solution of differential equation ( frac{dy}{dx} = frac{y}{x} + tan frac{y}{x} ) is ______

A. (cot( frac{y}{x}) = xc )
B. (cos( frac{y}{x}) = xc )
C. (sec^2( frac{y}{x}) = xc )
D. (sin( frac{y}{x}) = xc )
Answer» E.
Discussion
3.

Solve the differential equation ( frac{dy}{dx} = frac{x^2+y^2}{3xy} ) is _______

A. xp=(x<sup>2</sup>+2y<sup>2</sup>)<sup>-3</sup>
B. x<sup>2</sup> p=(x<sup>2</sup>-2y<sup>2</sup>)<sup>3</sup>
C. x<sup>4</sup> p=(x<sup>2</sup>-2y<sup>2</sup>)<sup>-3</sup>
D. x<sup>6</sup> p=(x<sup>2</sup>+2y<sup>2</sup>)<sup>3</sup>
Answer» C. x<sup>4</sup> p=(x<sup>2</sup>-2y<sup>2</sup>)<sup>-3</sup>
Discussion
4.

Solution of the differential equation (xy frac{dy}{dx} = 1+x+y+xy ) is ______

A. (y-x)-log(x(1+y))=c
B. log(x(1+y))=c
C. (y+x)-log(x)=c
D. (y-x)-log(y(1+x))=c
Answer» B. log(x(1+y))=c
Discussion
5.

Solution of the differential equation ( frac{dy}{dx} = (4x+2y+1)^2 ) is ______

A. ( frac{1}{2 sqrt{2}} tan^{-1} u2061( frac{4x+2y+1}{ sqrt{2}})=x+c )
B. ( frac{1}{ sqrt{2}} cot^{-1} u2061(4x+2y+1)=x+c )
C. ( frac{1}{ sqrt{2}} tan^{-1} u2061 u2061( frac{4x+2y+1}{ sqrt{2}})=c )
D. cot<sup>-1</sup> u2061 u2061 u2061(4x+2y+1)=x+c
Answer» B. ( frac{1}{ sqrt{2}} cot^{-1} u2061(4x+2y+1)=x+c )
Discussion
6.

Solution of the differential equation sec2 x tan y dx + sec2 y tan x dy=0 is _______

A. (sec x. sec y)=k
B. (sec x .tany)=k
C. (tan x. tany)=k
D. (sec x .tan x)+(sec y .tan y)=k
Answer» D. (sec x .tan x)+(sec y .tan y)=k
Discussion
7.

Solution of the differential equation ( frac{dy}{dx} = e^{3x-2y} + x^2 e^{-2y} ) is ______

A. ( frac{e^{2y}}{3} = frac{e^{3x}}{3} + frac{x^2}{2} + c )
B. ( frac{e^{3y} (e^{2x}+x^3)}{6} + c )
C. ( frac{e^{2y} (e^{3x}+x^3)}{6} + c )
D. ( frac{e^{2y}}{2} = frac{e^{3x}}{3} + frac{x^3}{3} + c )
Answer» E.
Discussion
8.

Solution of the differential equation ( frac{dy}{dx} = frac{y(x-y ln y)}{x(x ln x-y)} ) is _____________

A. ( frac{x ln u2061x+y ln u2061y}{xy} = c )
B. ( frac{x ln u2061x-y ln u2061y}{xy} = c )
C. ( frac{ln u2061x}{x} + frac{ln u2061y}{y} = c )
D. ( frac{ln u2061x}{x} frac{ln u2061y}{y} = c )
Answer» B. ( frac{x ln u2061x-y ln u2061y}{xy} = c )
Discussion