What is a solution to the differential equation $\frac{d y}{d x} = 3 x^{2} e^{- y}$ $dy/dx=3x^2e^-y$ ?

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Answer 1 · 2016-07-14T09:00:06

$y = ln (x^{3} + C)$ $y=ln (x^3 + C)$

$\frac{d y}{d x} = 3 x^{2} e^{- y}$ $dy/dx=3x^2e^-y$

separate it

$e^{y} \frac{d y}{d x} = 3 x^{2}$ $e^y dy/dx=3x^2$

$int \ e^y dy/dx \ dx=int \ 3x^2 \ dx$

$int \ e^y \ dy=int \ 3x^2 \ dx$

$e^y=x^3 + C$

$y=ln (x^3 + C)$

What is a solution to the differential equation dy/dx=3x^2e^-ydydx=3x2e−ydy/dx=3x^2e^-y?