Internal problem ID [3636]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 908.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 5.61 (sec). Leaf size: 121
dsolve(x^2*diff(y(x),x)^2-4*x*(2+y(x))*diff(y(x),x)+4*(2+y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -2 \\ y \relax (x ) = \frac {\left (-\frac {2 \sqrt {2}\, \sqrt {c_{1} x^{2}}}{x^{2}}+1\right ) x^{2}}{c_{1}} \\ y \relax (x ) = \frac {\left (\frac {2 \sqrt {2}\, \sqrt {c_{1} x^{2}}}{x^{2}}+1\right ) x^{2}}{c_{1}} \\ y \relax (x ) = -\frac {2 c_{1} \left (x \sqrt {2}-4 c_{1}\right )+8 c_{1}^{2}-x^{2}}{c_{1}^{2}} \\ y \relax (x ) = -\frac {-2 c_{1} \left (x \sqrt {2}+4 c_{1}\right )+8 c_{1}^{2}-x^{2}}{c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.206 (sec). Leaf size: 69
DSolve[x^2 (y'[x])^2-4 x(2+y[x])y'[x]+4(2+y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-c_1} x \left (x-2 \sqrt {2} e^{\frac {c_1}{2}}\right ) \\ y(x)\to e^{c_1} x^2-2 \sqrt {2} e^{\frac {c_1}{2}} x \\ y(x)\to -2 \\ y(x)\to 0 \\ \end{align*}