solve-y-2y-3-y-2-

Question Number 185526 by Matica last updated on 23/Jan/23

s o l v e y^{″} = (2 y + 3) {(y^{'})}^{2}

Answered by mr W last updated on 23/Jan/23

y^{″} = y^{'} \frac{{d y}^{'}}{d y}

y^{'} \frac{{d y}^{'}}{d y} = (2 y + 3) {(y^{'})}^{2}

\frac{{d y}^{'}}{y^{'}} = (2 y + 3) d y

\ln y^{'} = y^{2} + 3 y + C_{1}

y^{'} = {C e}^{y^{2} + 3 y}

\frac{d y}{d x} = {C e}^{y^{2} + 3 y}

\frac{d y}{e^{y^{2} + 3 y}} = C d x

\int \frac{d y}{e^{y^{2} + 3 y}} = C x + D

\Rightarrow \frac{e^{\frac{9}{4}} \sqrt{π}}{2} e r f (y + \frac{3}{2}) = C x + D

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