What is the solution for (dy)/(dx)=9xe^y,y(0)=0 ?

The solution for (dy)/(dx)=9xe^y,y(0)=0 is y=-ln(-(9x^2)/2+1)

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(dy)/(dx)=9xe^y,y(0)=0

\frac{d y}{d x} = 9 x e^{y}, y (0) = 0

y = - ln (- \frac{9 x ^{2}}{2} + 1)

Solution steps

\frac{d y}{d x} = 9 x e^{y}

Solve separable ODE:

y = - ln (- \frac{9 x ^{2}}{2} + 1)

y = - ln (- \frac{9 x ^{2}}{2} + 1)

f (x) = 2 x^{2} - 1, at x = - 1

\frac{d y}{d x} = x^{2} y - y + x^{2} - 1

\int 3 x^{4} d x

\frac{1}{s ^{2} ( s ^{2} + 1 )}

\frac{d}{d x} (- \frac{2 x}{( x ^{2} + 4 ) ^{2}})

What is the solution for (dy)/(dx)=9xe^y,y(0)=0 ?
The solution for (dy)/(dx)=9xe^y,y(0)=0 is y=-ln(-(9x^2)/2+1)