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

Answer: (x+1)(e^y-2)=C. Solution: Separate variables: dy/(2e^(-y)-1) = dx/(x+1). Multiply numerator and denominator by e^y: (e^y dy)/(2-e^y) = dx/(x+1). Integrating, -, 2-e^y, =, x+1, + k, so (x+1)(e^y-2) = C.

Calculus

Differential Equations

Medium

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

(where C is an arbitrary constant)

$e^y(x+1)=C$

$x(e^y-2)=C$

$(x+1)(e^y-2)=C$

$xe^y+2x=C$

✅ Correct Option: 3

Separate variables: $\dfrac{dy}{2e^{-y}-1} = \dfrac{dx}{x+1}$ .

Multiply numerator and denominator by $e^y$ : $\dfrac{e^y dy}{2-e^y} = \dfrac{dx}{x+1}$ .

Integrating, $-\log|2-e^y| = \log|x+1| + k$ , so $(x+1)(e^y-2) = C$ .

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The particular solution of the differential equation $\left[x \sin^2\left(\frac{y}{x}\right) - y\right]dx + xdy = 0$ , $y = \frac{\pi}{4}$ when $x = 1$ is

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If the order and degree of the differential equation $\sqrt{\frac{d^2y}{dx^2}} = \left(1 + \frac{dy}{dx}\right)^{\frac{1}{3}}$ are $a$ and $b$ respectively, then the value of $a^2 + b^2$ is

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For the differential equation $x\frac{dy}{dx} + 2y = x^2\log_e x$

(A) Integrating factor is $2x$

(B) Integrating factor is $x^2$

(D) General Solution is $y = \frac{x^4}{16}(4\log_e|x| - 1) + C$ Where C is an arbitrary constant.

Choose the correct answer from the options given below:

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The general solution of the differential equation $(y-x)dy + (x+y)dx = 0$ is: (where C is arbitrary constant)

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The solution of the differential equation $\frac{dy}{dx} = (1 + x^2)(1 + y^2)$ is (Here C is an arbitrary constant)

2026: 19 May Shift 1

Match List-I with List-II

List-I (Differential equation)	List-II (Integrating factor)
(A) $\frac{dy}{dx} + 2y = x$	(I) $e^x$
(B) $\frac{dy}{dx} + \left(\frac{2}{x}\right)y = x^2$	(II) $e^{2x}$
(C) $\frac{dy}{dx} - \left(\frac{2}{x}\right)y = \sin x$	(III) $\frac{1}{x^2}$
(D) $\frac{dy}{dx} + y = e^{-x}$	(IV) $x^2$

Choose the correct answer from the options given below:

The general solution of the differential equation (x+1)dydx=2e−y−1(x+1)\dfrac{dy}{dx}=2e^{-y}-1(x+1)dxdy​=2e−y−1 is: (where C is an arbitrary constant)

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CUET Mathematics Past Year Questions (Topic-Wise)

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

(where C is an arbitrary constant)