What is the solution for e^y(dy)/(dx)-x^2=0,y(0)=0 ?

The solution for e^y(dy)/(dx)-x^2=0,y(0)=0 is y=ln((x^3)/3+1)

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e^y(dy)/(dx)-x^2=0,y(0)=0

e^{y} \frac{d y}{d x} - x^{2} = 0, y (0) = 0

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

Solution steps

e^{y} \frac{d y}{d x} - x^{2} = 0

Solve separable ODE:

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

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

\frac{d v}{d t} = 60 - \frac{9}{100} \cdot v

e^{y} y^{^{'}} = \frac{( ln ( t ) ) ^{2}}{t}, y (1) = ln (8)

y^{^{'}} = - (x + 2) y^{2}

(3 t^{2} + 5) y^{^{'}} = 3 t y, y (0) = 8

\frac{d y}{d x} = \frac{x ^{3}}{y ^{3}}

What is the solution for e^y(dy)/(dx)-x^2=0,y(0)=0 ?
The solution for e^y(dy)/(dx)-x^2=0,y(0)=0 is y=ln((x^3)/3+1)