The general solution of differential equation d y-d x-ex-y-x2 e-y is

The correct option is B dy/dx=e^ y(e^x+x^2) ⇒ e^y dy=(e^x+x^2) dx ⇒∫ e^y dy= ∫(e^x+x^2)dx e^y=e^x+x^3/3+C ...

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integrating Factor

The general s...

Question

The general solution of differential equation $\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}$ is

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A

$\frac{d y}{d x} = e^{- y} (e^{x} + x^{2}) \Rightarrow e^{y} d y = (e^{x} + x^{2}) d x \Rightarrow \int e^{y} d y = \int (e^{x} + x^{2}) d x e^{y} = e^{x} + \frac{x^{3}}{3} + C$

Suggest Corrections

Similar questions

Q. The general solution of the differential equation

\frac{d y}{d x} = e^{x + y}

is :

Q. Solve the following differential equation:

\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}

Q. Solution of the differential equation

\frac{d y}{d x} = 2 e^{x - y} + x^{2} e^{- y}

Q. Find the solution of

\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}

The general solution of the differential equation $\frac{d y}{d x} = e^{x + y}$ is
(a) $e^{x} + e^{- y} = C$
(b) $e^{x} + e^{y} = C$
(c) $e^{- x} + e^{y} = C$
(d) $e^{- x} + e^{- y} = C$

Join BYJU'S Learning Program

The general solution of differential equation dydx=ex−y+x2e−y is

The correct option is A dydx=e−y(ex+x2)⇒eydy=(ex+x2)dx⇒∫eydy=∫(ex+x2)dxey=ex+x33+C

The general solution of differential equation $\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}$ is

The correct option is A

$\frac{d y}{d x} = e^{- y} (e^{x} + x^{2}) \Rightarrow e^{y} d y = (e^{x} + x^{2}) d x \Rightarrow \int e^{y} d y = \int (e^{x} + x^{2}) d x e^{y} = e^{x} + \frac{x^{3}}{3} + C$