Internal problem ID [8246]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 666.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\left (-\ln \relax (y)+1+x^{2}+x^{3}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 24
dsolve(diff(y(x),x) = (-ln(y(x))+1+x^2+x^3)*y(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{{\mathrm e}^{-x} c_{1}+x^{3}-2 x^{2}+4 x -3} \]
✓ Solution by Mathematica
Time used: 0.372 (sec). Leaf size: 27
DSolve[y'[x] == (1 + x^2 + x^3 - Log[y[x]])*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x ((x-2) x+4)-c_1 e^{-x}-3} \\ \end{align*}