Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 7 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.

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
2.

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

A. xp=(x2+2y2)-3
B. x2 p=(x2-2y2)3
C. x4 p=(x2-2y2)-3
D. x6 p=(x2+2y2)3
Answer» C. x4 p=(x2-2y2)-3
Discussion
3.

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
4.

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

A. \(\frac{1}{2\sqrt{2}} tan^{-1}⁡(\frac{4x+2y+1}{\sqrt{2}})=x+c \)
B. \(\frac{1}{\sqrt{2}} cot^{-1}⁡(4x+2y+1)=x+c \)
C. \(\frac{1}{\sqrt{2}} tan^{-1}⁡⁡(\frac{4x+2y+1}{\sqrt{2}})=c \)
D. cot-1⁡⁡⁡(4x+2y+1)=x+c
Answer» B. \(\frac{1}{\sqrt{2}} cot^{-1}⁡(4x+2y+1)=x+c \)
Discussion
5.

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
6.

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
7.

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

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