33.8 problem 970

Internal problem ID [4203]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 33
Problem number: 970.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

\[ \boxed {y^{2} {y^{\prime }}^{2}=a^{2}} \]

Solution by Maple

Time used: 0.016 (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: 0.285 (sec). Leaf size: 85

DSolve[y[x]^2(y'[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*}