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})

x \to \infty lim (e^{7 x})

(9 - x^{2})^{- \frac{1}{2}}

y = 2 x^{2} + 9 x - 7

\frac{\partial}{\partial x} (x^{8} y^{9} - x^{7} y^{8})

\frac{d}{d x} (2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

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})