f-x-1-f-x-2-f-x-

Question Number 128156 by DomaPeti last updated on 04/Jan/21

f {(x)}^{″} = \frac{1}{f {(x)}^{2}}

f (x) = ?

Answered by mr W last updated on 05/Jan/21

l e t y^{'} = u

y^{″} = u \frac{d u}{d y} = \frac{1}{y^{2}}

u d u = \frac{d y}{y^{2}}

\frac{u^{2}}{2} = - \frac{1}{y} + C_{1}

u = \frac{d y}{d x} = \pm \sqrt{2 (C_{1} - \frac{1}{y})}

\frac{d y}{\sqrt{C_{1} - \frac{1}{y}}} = \pm \sqrt{2} d x

\int \frac{d y}{\sqrt{C_{1} - \frac{1}{y}}} = C_{2} \pm \sqrt{2} x

\dots \dots

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