General solution of the differential equation dy/dx=e^x^2/2+xy is: (where C is an arbitrary constant) Option 1: y=Ce^x^2/2 Option 2: y=Ce^-x^2/2 Option 3: y=(C-x)e^x^2/2 Option 4: y=(x+C)e^x^2/2

The answer is 'y=(x+C)e^x^2/2'. View full solution:

CUET Mathematics - General solution of the differential equation dy/dx=e^x^2/2+xy is: (where C is an arbitrary constant) | PYQs + Solutions

CUET Mathematics 2026 22nd May Shift 1

Calculus

Medium

core

$y=Ce^{\frac{x^2}{2}}$

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

$y=(C-x)e^{\frac{x^2}{2}}$

$y=(x+C)e^{\frac{x^2}{2}}$

✅ Correct Option: 4

Related questions:

19 May Shift 1

Match List-I with List-II

List-I	List-II
Differential Equation	Integrating Factor
(A) $y dx + (x - y^3)dy = 0$	(I) $e^{-x}$
(B) $x\frac{dy}{dx} + y = x^2$	(II) $\frac{1}{x}$
(C) $\frac{dy}{dx} - y = e^x$	(III) $y$
(D) $x dy - y dx = x^3 dx$	(IV) $x$

Choose the correct answer from the options given below:

29th May Shift 1

The general solution of the differential equation $(x+1)\dfrac{dy}{dx}=2e^{-y}-1$ is:

(where C is an arbitrary constant)

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:

CUET Mathematics 2026 22nd May Shift 1 PYQs

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