Internal problem ID [12275]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises page 14
Problem number: 36.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {{y^{\prime }}^{2}-9 y x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 101
dsolve(diff(y(x),x)^2-9*x*y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = -x^{3}-2 \left (-x^{2}-\sqrt {c_{1} x}\right ) x +c_{1} y \left (x \right ) = -x^{3}-2 \left (-x^{2}+\sqrt {c_{1} x}\right ) x +c_{1} y \left (x \right ) = -x^{3}+2 \left (x^{2}-\sqrt {c_{1} x}\right ) x +c_{1} y \left (x \right ) = -x^{3}+2 \left (x^{2}+\sqrt {c_{1} x}\right ) x +c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 46
DSolve[(y'[x])^2-9*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 x^{3/2}+c_1\right ){}^2 y(x)\to \frac {1}{4} \left (2 x^{3/2}+c_1\right ){}^2 y(x)\to 0 \end{align*}