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

Answer: e^y - e^x = x^3 + C. Solution: Write the equation as dy/dx=e^(-y)(e^x+3x^2). Separating variables, e^y dy=(e^x+3x^2) dx, so e^y=e^x+x^3+C, that is e^y-e^x=x^3+C.

Calculus

Differential Equations

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Solution of differential equation $\frac{dy}{dx} = e^{x-y} + 3x^2 e^{-y}$ is:

(where C is an arbitrary constant)

$e^y + e^x = x^3 + C$

$e^y - e^x = x^3 + C$

$e^{x-y} = x^3 + C$

$e^x - e^y = 3x^3 + C$

✅ Correct Option: 2

Write the equation as $\frac{dy}{dx}=e^{-y}(e^x+3x^2)$ . Separating variables, $e^y\,dy=(e^x+3x^2)\,dx$ , so $e^y=e^x+x^3+C$ , that is $e^y-e^x=x^3+C$ .

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The solution of the differential equation $\frac{dr}{dt} = -rt, r(0) = r_0$ is

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The order and degree of the differential equation $\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}$ are

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Match List-I with List-II

List-I	List-II
(A) The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{dy}{dx}\right)$	(I) 4
(B) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^{1/4} + x^{1/5} = 0$	(II) 1
(C) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + 6y^5 = 0$	(III) Not defined
(D) The degree of differential equation $1 + \left(\frac{dy}{dx}\right)^4 = 7\left(\frac{d^2y}{dx^2}\right)^3$	(IV) 3

Choose the correct answer from the options given below:

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Which of the following differential equations has $y=x$ as one of the particular solution?

Solution of differential equation dydx=ex−y+3x2e−y\frac{dy}{dx} = e^{x-y} + 3x^2 e^{-y}dxdy​=ex−y+3x2e−y is: (where C is an arbitrary constant)

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CUET Mathematics Past Year Questions (Topic-Wise)

Solution of differential equation $\frac{dy}{dx} = e^{x-y} + 3x^2 e^{-y}$ is:

(where C is an arbitrary constant)