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

The answer is '(x+1)(e^y-2)=C'. View full solution:

CUET Mathematics - The general solution of the differential equation (x+1)dy/dx=2e^-y-1 is: (where C is an arbitrary constant) | PYQs + Solutions

CUET Mathematics 2026 29th May Shift 1

Calculus

Medium

common

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

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

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

$xe^y+2x=C$

✅ Correct Option: 3

Related questions:

12th May Shift 2

The general solution of the differential equation $\dfrac{dy}{dx} = 1+x+y+xy$ is: (where $C$ is an arbitrary constant)

(A) $1+y = x+\dfrac{x^2}{2}+C$

(B) $\log_e|1+y|^2 = x^2+2x+C$

(D) $\log_e|1+y| = x+\dfrac{x^2}{2}+C$

Choose the correct answer from the options given below:

23 Aug Shift 1

Match List - I with List - II

List - I (Differential Equation)	List - II (Degree)
A. $\left[1 + (y')^2\right]^2 = y''$	I. $2$
B. $\left[1 + (y'')^3\right]^{\frac{1}{2}} = (y')^3$	II. $4$
C. $(y''')^2 + y'' + 3y' + 5y = e^x$	III. $1$
D. $\left[1 + (y')^3\right]^{\frac{1}{2}} = (y'')^2$	IV. $3$

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15th May Shift 1

If $c$ is an arbitrary constant, then

Match the LIST-I with LIST-II

	LIST-I (Differential Equation)		LIST-II (Solution)
A.	$\dfrac{dy}{dx} = 1 + x + y + xy$	I.	$\log_e \vert y \vert = 2x + \log_e (x-1)^2 + c$
B.	$(x-1)\dfrac{dy}{dx} = 2xy$	II.	$y = cx$
C.	$\dfrac{dy}{dx} = 1 - x + y - xy$	III.	$\log_e \vert 1+y \vert = x + \dfrac{x^2}{2} + c$
D.	$x\,dy = y\,dx$	IV.	$\log_e \vert 1+y \vert = x - \dfrac{x^2}{2} + c$

Choose the correct answer from the options given below: