Internal problem ID [2320]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 7.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2} {y^{\prime }}^{2}+x y y^{\prime }=2 x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
dsolve(y(x)^2*diff(y(x),x)^2+x*y(x)*diff(y(x),x)-2*x^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {x^{2}+c_{1}} y \left (x \right ) = -\sqrt {x^{2}+c_{1}} y \left (x \right ) = \sqrt {-2 x^{2}+c_{1}} y \left (x \right ) = -\sqrt {-2 x^{2}+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 80
DSolve[y[x]^2*y'[x]^2+x*y[x]*y'[x]-2*x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {-x^2+c_1} y(x)\to \sqrt {2} \sqrt {-x^2+c_1} y(x)\to -\sqrt {x^2+2 c_1} y(x)\to \sqrt {x^2+2 c_1} \end{align*}