Internal problem ID [3640]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 912.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 15.812 (sec). Leaf size: 125
dsolve(x^2*diff(y(x),x)^2+(2*x-y(x))*y(x)*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 4 x \\ y \relax (x ) = 0 \\ y \relax (x ) = -\frac {2 c_{1}^{2} \left (\sqrt {2}\, c_{1}-x \right )}{-x^{2}+2 c_{1}^{2}} \\ y \relax (x ) = \frac {2 c_{1}^{2} \left (\sqrt {2}\, c_{1}+x \right )}{-x^{2}+2 c_{1}^{2}} \\ y \relax (x ) = -\frac {c_{1}^{2} \left (\sqrt {2}\, c_{1}-2 x \right )}{2 \left (-2 x^{2}+c_{1}^{2}\right )} \\ y \relax (x ) = \frac {c_{1}^{2} \left (\sqrt {2}\, c_{1}+2 x \right )}{-4 x^{2}+2 c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.646 (sec). Leaf size: 61
DSolve[x^2 (y'[x])^2+(2 x-y[x])y[x] y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {4 e^{-2 c_1}}{2+e^{2 c_1} x} \\ y(x)\to \frac {1}{-4 e^{4 c_1} x-2 e^{2 c_1}} \\ y(x)\to 0 \\ y(x)\to 4 x \\ \end{align*}