Internal problem ID [4144]
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]
\[ \boxed {{y^{\prime }}^{2} x^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 137
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 \left (x \right ) &= -2 \\ y \left (x \right ) &= \frac {2 \sqrt {2}\, \sqrt {c_{1} x^{2}}+x^{2}}{c_{1}} \\ y \left (x \right ) &= \frac {-2 \sqrt {2}\, \sqrt {c_{1} x^{2}}+x^{2}}{c_{1}} \\ y \left (x \right ) &= \frac {\left (-8 c_{1}^{2}+x^{2}\right ) \left (-2 \sqrt {2}\, c_{1} +x \right ) x}{\left (-4 \sqrt {2}\, c_{1} x +8 c_{1}^{2}+x^{2}\right ) c_{1}^{2}} \\ y \left (x \right ) &= \frac {\left (-8 c_{1}^{2}+x^{2}\right ) \left (2 \sqrt {2}\, c_{1} +x \right ) x}{\left (4 \sqrt {2}\, c_{1} x +8 c_{1}^{2}+x^{2}\right ) c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.233 (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*}