Internal problem ID [8334]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 754.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x) = (x*y(x)+x^3+x*y(x)^2+y(x)^3)/x^2,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a} \right )+x +c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 47
DSolve[y'[x] == (x^3 + x*y[x] + x*y[x]^2 + y[x]^3)/x^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+1\&,\frac {\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2+2 \text {$\#$1}}\&\right ]=x+c_1,y(x)\right ] \]