Internal problem ID [7373]
Book: First order enumerated odes
Section: section 1
Problem number: 57.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {{y^{\prime }}^{2}-\frac {1}{y^{3} x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 29
dsolve(diff(y(x),x)^2=1/(x^2*y(x)^3),y(x), singsol=all)
\begin{align*} \ln \left (x \right )-\frac {2 y \left (x \right )^{\frac {5}{2}}}{5}-c_{1} &= 0 \\ \ln \left (x \right )+\frac {2 y \left (x \right )^{\frac {5}{2}}}{5}-c_{1} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.139 (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*}