Internal problem ID [8019]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 439.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}+3 x y y^{\prime }+3 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(x^2*diff(y(x),x)^2+3*x*y(x)*diff(y(x),x)+3*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {c_{1} x^{-\frac {i \sqrt {3}}{2}}}{x^{\frac {3}{2}}} \\ y \relax (x ) = \frac {c_{1} x^{\frac {i \sqrt {3}}{2}}}{x^{\frac {3}{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 54
DSolve[3*y[x]^2 + 3*x*y[x]*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^{-\frac {3}{2}-\frac {i \sqrt {3}}{2}} \\ y(x)\to c_1 x^{\frac {1}{2} i \left (\sqrt {3}+3 i\right )} \\ y(x)\to 0 \\ \end{align*}