Calculus

Differential Equations

Medium

core

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(C) second order and second degree

(D) second order

Choose the correct answer from the options given below :

(D) Only

(B) and (D) Only

(A) Only

✅ Correct Option: 3

Two arbitrary constants imply order $= 2$ .

Differentiating twice gives a polynomial in $y''$ of degree 1.

Hence (B) second order and first degree, and (D) second order both hold.

2026: 31 May Shift 2

If $m$ and $n$ are respectively order and degree of the differential equation

$\left(\dfrac{d^2y}{dx^2}\right)^5 + 6\cdot\dfrac{\left(\dfrac{d^2y}{dx^2}\right)^3}{\dfrac{d^3y}{dx^3}} + \dfrac{d^3y}{dx^3} = x^2+5$ then :

2025: 13 May Shift 1

The general solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = ax + by$ is

2025: 13 May Shift 2

The general solution of differential equation $\frac{dy}{dx} = e^{x+y}$ is

2025: 26 May Shift 2

Match List-I with List-II

List-I	List-II
Differential Equations	Order and degree
(A) $ydx + x\log(y/x)dy - 2xdy = 0$	(I) Order : 2, degree:1
(B) $\left(\frac{d^3y}{dx^3}\right)^2 + 3\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^4 = y^2$	(II) Order :1, degree:1
(C) $\frac{dy}{dx} + \log\left(\frac{dy}{dx}\right) + x = y$	(III) Order : 3, degree:2
(D) $\left(\frac{ds}{dt}\right)^4 + 2s\frac{d^2s}{dt^2} = 0$	(IV) Order : 1, degree: Not defined

Choose the correct answer from the options given below:

2026: 18 May Shift 1

Match List-I with List-II

Choose the correct answer from the options given below:

2025: 2 June Shift 1

The integrating factor of the differential equation $\frac{dy}{dx} = x + xy$ is

The differential equation whose solution is Ax2+By2=1Ax^2 + By^2 = 1Ax2+By2=1 where A and B are arbitrary constant is of : (A) first order and first degree (B) second order and first degree (C) second order and second degree (D) second order Choose the correct answer from the options given below :