Internal problem ID [3342]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 600.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x^{2}-y^{2}\right ) y^{\prime }-2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 45
dsolve((x^2-y(x)^2)*diff(y(x),x) = 2*x*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-1+\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ y \relax (x ) = \frac {1+\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.486 (sec). Leaf size: 66
DSolve[(x^2-y[x]^2)y'[x]==2 x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x^2+e^{2 c_1}}+e^{c_1}\right ) \\ y(x)\to 0 \\ \end{align*}