# Differential Equations

This is an MCQ-based quiz on Differential Equations.

This includes Order, Degree, Linear Equations, and Homogenous Equations.

Start Quiz

The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is

0.4 π cm/s 0.8 π cm/s 0.8 cm/s None of these

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

tan x + tan y = k tan x – tan y = k tan x / tan y = k tan x.tan y = k

Which of the following is a second order differential equation?

(y’)² + x = y² y’y” + y = sin x y” + (y”)² + y = 0 y’ = y²

Solution of differential equation xdy – ydx = Q represents

A rectangular hyperbola

Parabola whose vertex is at origin

Straight line passing through origin

A circle whose centre is at origin

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

0 2 3 4.

The number of arbitrary constants in the particular solution of a differential equation of third order is:

3 2 1 0

Which of the following is a homogeneous differential equation?

(4x + 6y + 5)dy – (3y + 2x + 4)dx = 0 xy dx – (x³ + y²)dy = Q (x³ + 2y²) dx + 2xy dy = 0 y² dx + (x² – xy – y²)dy = 0.

The general solution of the differential equation dy / dx = e^(x+y) is

e^x + e^-y = c e^x + e^y = c e^-x + e^y = c e^-x + e^-y = c.

The integrating factor of the differential equation x(dy / dx) – y = 2x² is

e^-x e^-y 1 / x x

The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is

an ellipse parabola circle rectangular hyperbola

Which of the following is the general solution of d^2y / dx^2 – 2*dy/dx + y = 0

y = (Ax + B)e^x y = (Ax + B)e^-x y = Ae^x + Be^-x y = A cos x + B sin x

Integrating factor of the differential equation dy/dx + y tan x – sec x = 0 is

cos x

sec x

tan x

sin x

Quiz/Test Summary
Title: Differential Equations
Questions: 12
Contributed by: 