What is the solution for (dy)/(dx)=7xe^y,y(0)=0 ?

The solution for (dy)/(dx)=7xe^y,y(0)=0 is y=-ln(-(7x^2)/2+1)

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(dy)/(dx)=7xe^y,y(0)=0

\frac{d y}{d x} = 7 x e^{y}, y (0) = 0

y = - ln (- \frac{7 x ^{2}}{2} + 1)

Solution steps

\frac{d y}{d x} = 7 x e^{y}

Solve separable ODE:

y = - ln (- \frac{7 x ^{2}}{2} + 1)

y = - ln (- \frac{7 x ^{2}}{2} + 1)

\frac{d}{d x} (- 3 cos^{2} (x) sin (x))

\int \frac{1}{x ( x ^{2} - 9 ) ^{\frac{3}{2}}} d x

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

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

x \to - 2 lim (3 x^{3} - 4 x + 2)

What is the solution for (dy)/(dx)=7xe^y,y(0)=0 ?
The solution for (dy)/(dx)=7xe^y,y(0)=0 is y=-ln(-(7x^2)/2+1)