29.33.8 problem 970

Internal problem ID [5547]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 970
Date solved : Monday, January 27, 2025 at 11:44:46 AM
CAS classification : [_quadrature]

\begin{align*} y^{2} {y^{\prime }}^{2}&=a^{2} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 49

dsolve(y(x)^2*diff(y(x),x)^2 = a^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 85

DSolve[y[x]^2(D[y[x],x])^2==a^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {2} \sqrt {-a x+c_1} \\ y(x)\to \sqrt {2} \sqrt {-a x+c_1} \\ y(x)\to -\sqrt {2} \sqrt {a x+c_1} \\ y(x)\to \sqrt {2} \sqrt {a x+c_1} \\ \end{align*}