What is the solution for y^{''}=13(y^')^2 ?

The solution for y^{''}=13(y^')^2 is y=-1/13 ln(13t+c_{1})+c_{2}

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y^{''}=13(y^')^2

y^{^{''}} = 13 (y^{^{'}})^{2}

y = - \frac{1}{13} ln (13 t + c_{1}) + c_{2}

Solution steps

y^{''} (t) = 13 (y^{'} (t))^{2}

Solve using substitution:

y = - \frac{1}{13} ln (13 t + c_{1}) + c_{2}

y = - \frac{1}{13} ln (13 t + c_{1}) + c_{2}

\int \frac{13}{x ( x ^{2} + 25 )} d x

\int_{3}^{11} \frac{1}{2 x + 3} d x

x^{\frac{9}{6}}

f (x) = - 10 x^{2} + 1760 x - 50000

f (t) = 9 t - 2 t^{2}

What is the solution for y^{''}=13(y^')^2 ?
The solution for y^{''}=13(y^')^2 is y=-1/13 ln(13t+c_{1})+c_{2}