Internal problem ID [8632]
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)]`]]
\[ \boxed {x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}=-x^{4}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 163
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 \left (x \right ) = \frac {x \left (x^{2} c_{1} -\sqrt {c_{1}^{2} x^{4}-c_{1} x^{4}+x^{2}}+x \right )}{x +2}+\frac {2 x^{2} c_{1} -2 \sqrt {c_{1}^{2} x^{4}-c_{1} x^{4}+x^{2}}+2 x}{x +2}-2 x^{2} c_{1} -x y \left (x \right ) = \frac {x \left (x^{2} c_{1} +\sqrt {c_{1}^{2} x^{4}-c_{1} x^{4}+x^{2}}+x \right )}{x +2}+\frac {2 x^{2} c_{1} +2 \sqrt {c_{1}^{2} x^{4}-c_{1} x^{4}+x^{2}}+2 x}{x +2}-2 x^{2} c_{1} -x \end{align*}
✓ Solution by Mathematica
Time used: 25.374 (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*}