Internal problem ID [6620]
Book: First order enumerated odes
Section: section 1
Problem number: 57.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-\frac {1}{x^{2} y^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.407 (sec). Leaf size: 29
dsolve(diff(y(x),x)^2=1/(x^2*y(x)^3),y(x), singsol=all)
\begin{align*} \ln \relax (x )-\frac {2 y \relax (x )^{\frac {5}{2}}}{5}-c_{1} = 0 \\ \ln \relax (x )+\frac {2 y \relax (x )^{\frac {5}{2}}}{5}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 45
DSolve[(y'[x])^2==1/(x^2*y[x]^3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {5}{2}\right )^{2/5} (-\log (x)+c_1){}^{2/5} \\ y(x)\to \left (\frac {5}{2}\right )^{2/5} (\log (x)+c_1){}^{2/5} \\ \end{align*}