What is the solution for (dy)/(dx)=e^{x-y}+x^2e^{-y} ?

The solution for (dy)/(dx)=e^{x-y}+x^2e^{-y} is y=ln(e^x+(x^3)/3+c_{1})

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(dy)/(dx)=e^{x-y}+x^2e^{-y}

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

y = ln (e^{x} + \frac{x ^{3}}{3} + c_{1})

Solution steps

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

Solve separable ODE:

y = ln (e^{x} + \frac{x ^{3}}{3} + c_{1})

y = ln (e^{x} + \frac{x ^{3}}{3} + c_{1})

y^{^{'}} + 0.2 t y = 6 t

y^{^{'}} = 7 y - 8

5 x - 5 x cos (y) d x + x sin (y) d y = 0

\frac{d y}{d x} = x^{2} y - 3 y + x^{2} - 3

\frac{d y}{d x} = \frac{- 0.8}{cos ( y )}, y (0) = \frac{π}{3}

What is the solution for (dy)/(dx)=e^{x-y}+x^2e^{-y} ?
The solution for (dy)/(dx)=e^{x-y}+x^2e^{-y} is y=ln(e^x+(x^3)/3+c_{1})