Internal problem ID [8777]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 441.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 y \left (y+2\right )=0} \]
✓ Solution by Maple
Time used: 1.266 (sec). Leaf size: 137
dsolve(x^2*diff(y(x),x)^2-4*x*(y(x)+2)*diff(y(x),x)+4*y(x)*(y(x)+2) = 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 c_{1} \sqrt {2}+x \right ) x}{\left (-4 c_{1} \sqrt {2}\, 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 c_{1} \sqrt {2}+x \right ) x}{\left (4 c_{1} \sqrt {2}\, x +8 c_{1}^{2}+x^{2}\right ) c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 69
DSolve[4*y[x]*(2 + y[x]) - 4*x*(2 + y[x])*y'[x] + x^2*y'[x]^2==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*}