Internal problem ID [4147]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 911.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x^{2} {y^{\prime }}^{2}+\left (y+2 x \right ) y y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = -4 x y \left (x \right ) = 0 y \left (x \right ) = \frac {2 c_{1}^{2} \left (\sqrt {2}\, c_{1} -x \right )}{2 c_{1}^{2}-x^{2}} y \left (x \right ) = -\frac {2 c_{1}^{2} \left (\sqrt {2}\, c_{1} +x \right )}{2 c_{1}^{2}-x^{2}} y \left (x \right ) = \frac {c_{1}^{2} \left (\sqrt {2}\, c_{1} -2 x \right )}{2 c_{1}^{2}-4 x^{2}} y \left (x \right ) = -\frac {c_{1}^{2} \left (\sqrt {2}\, c_{1} +2 x \right )}{2 \left (c_{1}^{2}-2 x^{2}\right )} \end{align*}
✓ Solution by Mathematica
Time used: 0.698 (sec). Leaf size: 63
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 {e^{4 c_1}}{-x+e^{2 c_1}} y(x)\to \frac {e^{4 c_1}}{4 \left (4 x+e^{2 c_1}\right )} y(x)\to 0 y(x)\to -4 x \end{align*}