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Show that the solution of of the initial value problem \(u(0)=1\) of the differential equation \[ \left(\frac{d u}{d x}\right)^{2}=\frac{2}{9} \frac{x^{2}}{u^{3}} \] is given by

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Show that the solution of of the initial value problem \(u(0)=1\) of the differential equation
\[
\left(\frac{d u}{d x}\right)^{2}=\frac{2}{9} \frac{x^{2}}{u^{3}}
\]
is given by
\[
u(x)=\left(\frac{5}{6 \sqrt{2}}\left(x^{2}-1\right)+1\right)^{2 / 5}
\]
in Mathematics by ♦ Diamond (55,179 points) | 13 views

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