62.13.4 problem Ex 4

Internal problem ID [12879]
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
Date solved : Tuesday, January 28, 2025 at 04:31:38 AM
CAS classification : [_linear]

\begin{align*} \left (2 x y^{\prime }-y\right )^{2}&=8 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 30

dsolve((2*x*diff(y(x),x)-y(x))^2=8*x^3,y(x), singsol=all)
 

\begin{align*} y &= \left (-\sqrt {2}\, x +c_{1} \right ) \sqrt {x} \\ y &= \left (\sqrt {2}\, x +c_{1} \right ) \sqrt {x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 42

DSolve[(2*x*D[y[x],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*}