The solution of cos y (d y/d x)=ex+ sin y+x2 e sin y is f(x)+e- sin y=C(C is arbitrary real constant) where f(x) is equal to

Question

The solution of cos y (d y/d x)=ex+ sin y+x2 e sin y is f(x)+e- sin y=C(C is arbitrary real constant) where f(x) is equal to (A) ex+(1/2) x3 (B) e-x+(1/3) x3 (C) e-x+(1/2) x3 (D) ex+(1/3) x3

Tardigrade Admin · Accepted Answer

-e- sin y cos y (d y/d x)=-[ex+x2] ⇒ d(e- sin y)+(ex+x2) d x=0 ⇒ e- sin y+ex+(x3/3)=C

Q. The solution of $cos y \frac{d y}{d x} = e^{x + s i n y} + x^{2} e^{s i n y}$ is $f (x) + e^{- s i n y} = C (C$ is arbitrary real constant) where $f (x)$ is equal to

$e^{x} + \frac{1}{2} x^{3}$

$e^{- x} + \frac{1}{3} x^{3}$

$e^{- x} + \frac{1}{2} x^{3}$

$e^{x} + \frac{1}{3} x^{3}$

$- e^{- s i n y} cos y \frac{d y}{d x} = - [e^{x} + x^{2}]$
$\Rightarrow d (e^{- s i n y}) + (e^{x} + x^{2}) d x = 0$
$\Rightarrow e^{- s i n y} + e^{x} + \frac{x ^{3}}{3} = C$

Q. The solution of cosydxdy​=ex+siny+x2esiny is f(x)+e−siny=C(C is arbitrary real constant) where f(x) is equal to

ex+21​x3

e−x+31​x3

e−x+21​x3

ex+31​x3