Internal problem ID [10189]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
24. Equations solvable for \(p\). Page 49
Problem number: Ex 4.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (-y+2 y^{\prime } x \right )^{2}-8 x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 30
dsolve((2*x*diff(y(x),x)-y(x))^2=8*x^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\sqrt {2}\, x +c_{1}\right ) \sqrt {x} \\ y \relax (x ) = \left (\sqrt {2}\, x +c_{1}\right ) \sqrt {x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 42
DSolve[(2*x*y'[x]-y[x])^2==8*x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} \left (-\sqrt {2} x+c_1\right ) \\ y(x)\to \sqrt {x} \left (\sqrt {2} x+c_1\right ) \\ \end{align*}