Calculus

Differential Equations

Medium

core

The differential equation $y = xp + \sqrt{x^2 p^3 + 4}$ where $p = \frac{dy}{dx}$ is :

(A) of order 1

(B) of degree 1

(C) of order 2

(D) of degree 3

Choose the correct answer from the options given below :

(A) and (B) Only

(A) and (D) Only

(B) and (C) Only

✅ Correct Option: 2

Highest derivative is $p=dy/dx$ , so order is 1.

To find degree, isolate radical: $(y-xp)^2=x^2 p^3+4$ . Highest power of $p$ is 3, so degree is 3.

Hence (A) and (D) are correct.

2025: 15 May Shift 1

Consider the differential equation $\frac{dy}{dx} + y \tan x = \sec x$ , then which of the following statements are correct?

(A) It is homogeneous

(B) It has $\sec x$ as its integrating factor

(D) It's degree is not defined

Choose the correct answer from the options given below:

2024: 16 May Shift 1

The degree of the differential equation $\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}$ is :

2022: 25 May Shift 1

The degree of the differential equation

$\left(1 + \frac{dy}{dx}\right)^4 = \left(\frac{d^2y}{dx^2}\right)^2$ is:

2025: 21 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Degree of the differential equation $\frac{d^2y}{dx^2} = e^{dy/dx}$ is	(I) 2
(B) Order of the differential equation $(\frac{dy}{dx})^2 + \frac{d^3y}{dx^3} = 0$ is	(II) not defined
(C) Degree of the differential equation $\frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 - 5x^2 = 0$	(III) 3
(D) If p is the order and q is the degree of the differential equation $\frac{dy}{dx} + 3y = e^x$ , then p + q is	(IV) 1

Choose the correct answer from the options given below:

2025: 19 May Shift 1

The general solution of the differential equation $\frac{dy}{dx} = e^{ax+by}$ is: (Here C is an arbitrary constant)

2022: 4 Aug Shift 1

The solution of the differential equation $\frac{dy}{dx} = \frac{\lambda^2}{(x+y)^2}$ ( $\lambda$ is constant) is:

The differential equation y=xp+x2p3+4y = xp + \sqrt{x^2 p^3 + 4}y=xp+x2p3+4​ where p=dydxp = \frac{dy}{dx}p=dxdy​ is : (A) of order 1 (B) of degree 1 (C) of order 2 (D) of degree 3 Choose the correct answer from the options given below :