The solution of dy-dx-ex-y-e2logx-y

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

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Solving Linear Differential Equations of First Order

The solution ...

Question

The solution of $\frac{d y}{d x} = e^{x - y} + e^{2 l o g x - y}$

e^{y} = e^{x} + \frac{x^{2}}{3} + c

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

e^{y} = e^{x} + \frac{x^{3}}{3} + c

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

e^{y} = e^{x} + l o g x + c

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

y = \frac{e^{3 x + y}}{3}

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

Open in App

Solution

The correct option is B $e^{y} = e^{x} + \frac{x^{3}}{3} + c$
$\frac{d y}{d x} = e^{x - y} + e^{2 l o g x - y}$
$\Rightarrow e^{y} d y = (e^{x} + x^{2}) d x$
$\Rightarrow e^{y} = e^{x} + x^{3} / 3 + c$

Suggest Corrections

Similar questions

The solution of the equation $\frac{d y}{d x} - e^{x - y} + x^{2} e^{- y}$ is
[MP PET 2004]

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

Q. If

e^{x} + e^{y} = e^{x + y}

, show that

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

Q. If

e^{x} + e^{y} = e^{x + y}

, find

\frac{d y}{d x}

Q. Find

\frac{d y}{d x}

e^{x} + e^{y} = e^{x - y}

Join BYJU'S Learning Program

The solution of dydx=ex−y+e2logx−y

The correct option is B ey=ex+x33+cdydx=ex−y+e2log x−y⇒eydy=(ex+x2)dx⇒ey=ex+x3/3+c

The solution of $\frac{d y}{d x} = e^{x - y} + e^{2 l o g x - y}$

The correct option is B $e^{y} = e^{x} + \frac{x^{3}}{3} + c$
$\frac{d y}{d x} = e^{x - y} + e^{2 l o g x - y}$
$\Rightarrow e^{y} d y = (e^{x} + x^{2}) d x$
$\Rightarrow e^{y} = e^{x} + x^{3} / 3 + c$