Internal problem ID [8189]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 609.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-3 y x^{2}+F \left (y x^{3}\right )}{x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 22
dsolve(diff(y(x),x) = (-3*x^2*y(x)+F(x^3*y(x)))/x^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (x -\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1}\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.211 (sec). Leaf size: 117
DSolve[y'[x] == (F[x^3*y[x]] - 3*x^2*y[x])/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}-\frac {x^3+F\left (x^3 K[2]\right ) \int _1^x\left (\frac {3 K[1]^5 K[2] F'\left (K[1]^3 K[2]\right )}{F\left (K[1]^3 K[2]\right )^2}-\frac {3 K[1]^2}{F\left (K[1]^3 K[2]\right )}\right )dK[1]}{F\left (x^3 K[2]\right )}dK[2]+\int _1^x\left (1-\frac {3 K[1]^2 y(x)}{F\left (K[1]^3 y(x)\right )}\right )dK[1]=c_1,y(x)\right ] \]