Particular solution of the differential equation dy + 2xy^2 dx = 0, given that y=1, when x=0, is Option 1: y = x^2+1 Option 2: y = x^2-1 Option 3: y = 1/(x^2+1) Option 4: y = 1/(x^2-1)

Answer: y = 1/(x^2+1). Solution: Separating variables: dy/y^2=-2x dx, so -1/y=-x^2+C, i.e. 1/y=x^2-C. Using y=1 at x=0 gives C=-1, hence 1/y=x^2+1 and y=1/(x^2+1).

Calculus

Differential Equations

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Particular solution of the differential equation $dy + 2xy^2 dx = 0$ , given that $y=1$ , when $x=0$ , is

$y = x^2+1$

$y = x^2-1$

$y = \frac{1}{x^2+1}$

$y = \frac{1}{x^2-1}$

✅ Correct Option: 3

Separating variables: $\frac{dy}{y^2}=-2x\,dx$ , so $-\frac{1}{y}=-x^2+C$ , i.e. $\frac{1}{y}=x^2-C$ .

Using $y=1$ at $x=0$ gives $C=-1$ , hence $\frac{1}{y}=x^2+1$ and $y=\frac{1}{x^2+1}$ .

2023: 15 June Shift 2

The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2y}{dx^2}} = p$ is :

2025: 13 May Shift 1

Let the degree and order of the differential equation $2x^3\frac{dy}{dx}-5\left(\frac{d^2y}{dx^2}\right)^2=6\left(\frac{dy}{dx}\right)^3$ be $m$ and $n$ respectively. Then

(A) m = 2

(B) n = 3

(D) mn = 4

Choose the correct answer from the options given below:

2022: 4 Aug Shift 1

The sum of order and degree of differential equation $2x^2 \cdot \left(\frac{d^2y}{dx^2}\right) - 3 \cdot \left(\frac{dy}{dx}\right)^3 + y = 0$ is

2026: 21 May Shift 2

Match the differential equation (List-I) with its order and degree (List-II)

LIST-I		LIST-II
A. $\dfrac{d^3y}{dx^3} + x^2\left(\dfrac{d^2y}{dx^2}\right) = 0$		I. order =3; degree is not defined
B. $\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 0$		II. order =3; degree=1
C. $1 - \left(\dfrac{dy}{dx}\right)^2 = \left(a\dfrac{d^2y}{dx^2}\right)^{1/3}$		III. order =2; degree=1
D. $y = x\left(\dfrac{dy}{dx}\right)^3 + \left(\dfrac{d^2y}{dx^2}\right)^4$		IV. order =2; degree=4

Choose the correct answer from the options given below:

2022: 10 Aug Shift 1

The solution of differential equation $\sqrt{x+1} - \sqrt{x-1}\frac{dy}{dx} = 0$ is

2025: 21 May Shift 1

The general solution of the differential equation $x(1 + y^2)dx + y(1 + x^2)dy = 0$ is

Particular solution of the differential equation dy+2xy2dx=0dy + 2xy^2 dx = 0dy+2xy2dx=0, given that y=1y=1y=1, when x=0x=0x=0, is

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CUET Mathematics Past Year Questions (Topic-Wise)

Particular solution of the differential equation $dy + 2xy^2 dx = 0$ , given that $y=1$ , when $x=0$ , is