Calculus

Differential Equations

Medium

common

Which of the following statements are TRUE?

A. Order of the differential equation is the order of highest differential appearing in the differential equation.

B. Degree of a differential equation is a real number.

C. Order of a differential equation is whole number.

D. Degree of a differential equation is the degree of the highest order derivative, when differential coefficients are free from radicals and fractions.

Choose the correct answer from the options given below:

A and D only

B and C only

A, B, C and D

B, C and D only

✅ Correct Option: 3

Coming Soon!

2026: 12 May Shift 2

Match List-I with List-II

List-I (Differential Equation)	List-II (Order and degree)
(A) $\left(\dfrac{d^2y}{dx^2}\right)^2 + e^{\frac{dy}{dx}} = 0$	(I) order = 2, degree = 1
(B) $xy\dfrac{d^2y}{dx^2} + x\left(\dfrac{dy}{dx}\right)^2 - y\dfrac{dy}{dx} = 0$	(II) order = 2, degree = not defined
(C) $\left(\dfrac{d^3y}{dx^3}\right)^2 + \log_e\left(\dfrac{dy}{dx}\right) = 4x$	(III) order = 3, degree = 2
(D) $\dfrac{d}{dx}\left(\dfrac{d^2y}{dx^2}\right) + y\dfrac{dy}{dx} = \left(1+\dfrac{dy}{dx}\right)^{1/2}$	(IV) order = 3, degree = not defined

Choose the correct answer from the options given below:

2026: 14 May Shift 2

The solution of the differential equation $\frac{dy}{dx} = x^2 + x + \frac{1}{x}$ is

2026: 29 May Shift 1

The substitution $y=vx$ transforms the differential equation $xdy-ydx=\sqrt{x^2+y^2}dx$ into

2026: 18 May Shift 2

The order and degree of the differential equation $\left[2+\left(\dfrac{dy}{dx}\right)\right]^{5/2}=7\dfrac{d^3y}{dx^3}$ is

2022: 4 Aug Shift 1

Solution of the differential equation $\frac{dy}{dx} = x + xy - (1 + y)$ is:

2022: 6 Aug Shift 2

If the solution curve of the differentiable equation $\frac{dy}{dx} + 2y = e^{3x}$ , passes through the point $\left(0, \frac{6}{5}\right)$ , then the value of $y(\log_e 2)$ is:

Solution

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