The solution of the differential equation \frac{dy}{dx} = e{x+y} + x^2e^y is

Correct Answer is : ex+e−y+x33 = C

NIMCET 2017 Question Paper with solutions

Question : 118 of 120

Marks: +1, -0

The solution of the differential equation

{dy}/{dx}

e{x+y}

x^2e^y

Solution:

⇒

{dy}/e^x

= (

x^2+e^x

) dx [using variable separable form]
Integrating both sides, we get
∫

e^{-y}

= ∫

(x^2+e^x)

dx
⇒

-e^{-y}

x^3/3+e^x

+ C
⇒

e^x+e^{-y}

x^3/3

= C
[where C is constant]

Go to Question:

Prev Question

Next Question