57.1.57 problem 57

Internal problem ID [9041]
Book : First order enumerated odes
Section : section 1
Problem number : 57
Date solved : Monday, January 27, 2025 at 05:27:53 PM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{2}&=\frac {1}{x^{2} y^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.076 (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^{{5}/{2}}}{5}-c_{1} &= 0 \\ \ln \left (x \right )+\frac {2 y^{{5}/{2}}}{5}-c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 45

DSolve[(D[y[x],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*}