Internal problem ID [6618]
Book: First order enumerated odes
Section: section 1
Problem number: 56.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {{y^{\prime }}^{2}-\frac {1}{x y^{3}}=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 43
dsolve(diff(y(x),x)^2=1/(x*y(x)^3),y(x), singsol=all)
\begin{align*} \frac {\left (x y \left (x \right )\right )^{\frac {5}{2}}}{x^{\frac {5}{2}}}-5 \sqrt {x}-c_{1} = 0 \\ \frac {\left (x y \left (x \right )\right )^{\frac {5}{2}}}{x^{\frac {5}{2}}}+5 \sqrt {x}-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 53
DSolve[(y'[x])^2==1/(x*y[x]^3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {5}{2}\right )^{2/5} \left (-2 \sqrt {x}+c_1\right ){}^{2/5} \\ y(x)\to \left (\frac {5}{2}\right )^{2/5} \left (2 \sqrt {x}+c_1\right ){}^{2/5} \\ \end{align*}