Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 4 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.

Find the general solution of the D.E y = 2xy’ – 3(y’)2.

A. \(y(p) = p^{1/2} + \frac{c}{2p}\)
B. \(y(p) = p^2 + \frac{2c}{p}\)
C. \(x(p) = -cp + \frac{c}{p^2}\)
D. \(x(p) = 2p + \frac{2c}{p^2} \)
Answer» C. \(x(p) = -cp + \frac{c}{p^2}\)
Discussion
2.

Find the general solution of the D.E 2y-4xy’-log y’=0.

A. \(y(p) = \frac{2c}{p} – 1 + \frac{log⁡p}{2} \)
B. \(y(p) = \frac{c}{2p} – 2 + log⁡p\)
C. \(x(p) = \frac{-1}{p} + \frac{c}{p^2} \)
D. \(x(p) = \frac{1}{2p} + \frac{c}{p^{1/2}} \)
Answer» B. \(y(p) = \frac{c}{2p} – 2 + log⁡p\)
Discussion
3.

Find the general solution for the equation (px-py)(py+x)=2p by reducing into Clairaut’s form by using the substitution X=x2, Y=y2 where p=\(\frac{dy}{dx}\).

A. \(y^2 = x + \frac{c}{c+1}\)
B. \(y^2 = cx^2 – \frac{2c}{c+1}\)
C. \(x^2 = cy^2 – \frac{1}{2c+1}\)
D. \(x^2 = y^2 + \frac{c}{2c+2}\)
Answer» C. \(x^2 = cy^2 – \frac{1}{2c+1}\)
Discussion
4.

Singular solution for the Clairaut’s equation \(y = y’x+\frac{a}{y’}\) is given by _______

A. \(\frac{x^2}{a^2} + \frac{y^2}{a^2} = 1\)
B. y2=-4ax
C. y2=4ax
D. x2=-2ay
Answer» D. x2=-2ay
Discussion