Internal problem ID [7876]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 296.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {x \left (y^{2}+y x^{2}+x^{2}\right ) y^{\prime }-2 y^{3}-2 y^{2} x^{2}+x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 2.218 (sec). Leaf size: 159
dsolve(x*(y(x)^2+x^2*y(x)+x^2)*diff(y(x),x)-2*y(x)^3-2*x^2*y(x)^2+x^4=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-\frac {-c_{1} x +x^{2}+\sqrt {-x^{4} c_{1}+x^{4}+x^{2} c_{1}^{2}}}{x^{2} \left (x -2\right )}-1\right ) x^{3} \left (x -2\right )}{-c_{1} x +x^{2}+\sqrt {-x^{4} c_{1}+x^{4}+x^{2} c_{1}^{2}}} \\ y \relax (x ) = -\frac {\left (\frac {c_{1} x -x^{2}+\sqrt {-x^{4} c_{1}+x^{4}+x^{2} c_{1}^{2}}}{x^{2} \left (x -2\right )}-1\right ) x^{3} \left (x -2\right )}{c_{1} x -x^{2}+\sqrt {-x^{4} c_{1}+x^{4}+x^{2} c_{1}^{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 26.611 (sec). Leaf size: 88
DSolve[x*(y[x]^2+x^2*y[x]+x^2)*y'[x]-2*y[x]^3-2*x^2*y[x]^2+x^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{-c_1} \left (x^2+\sqrt {x^2 \left (x^2-e^{c_1} x^2+e^{2 c_1}\right )}\right ) \\ y(x)\to e^{-c_1} \left (-x^2+\sqrt {x^2 \left (x^2-e^{c_1} x^2+e^{2 c_1}\right )}\right ) \\ \end{align*}