The general solution of the differential equation (dy/dx)=ey(ex+e-x+2x) is

Question

The general solution of the differential equation (dy/dx)=ey(ex+e-x+2x) is (A)  e-y=ex-e-x+x2+C  (B)  e-y=e-x-ex-x2+C  (C)  e-y=-e-x-ex-x2+C  (D)  ey=e-x+ex+x2+C

Tardigrade Admin · Accepted Answer

(dy/dx)=ey(ex+e-x+2x) ⇒ e-ydy=(ex+e-x+2x)dx On integrating -e-y=ex-e-x+x2-C ⇒ e-y=e-x-ex-x2+C

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

$e^{- y} = e^{x} - e^{- x} + x^{2} + C$

$e^{- y} = e^{- x} - e^{x} - x^{2} + C$

$e^{- y} = - e^{- x} - e^{x} - x^{2} + C$

$e^{y} = e^{- x} + e^{x} + x^{2} + C$

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

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

Q. The general solution of the differential equation dxdy​=ey(ex+e−x+2x) is

e−y=ex−e−x+x2+C

e−y=e−x−ex−x2+C

e−y=−e−x−ex−x2+C

ey=e−x+ex+x2+C

ey=e−x+ex+C

dxdy​=ey(ex+e−x+2x) ⇒ e−ydy=(ex+e−x+2x)dx On integrating −e−y=ex−e−x+x2−C ⇒ e−y=e−x−ex−x2+C