Internal problem ID [8285]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 705.
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 }-\frac {\left (\ln \relax (y)+x +x^{3}+x^{4}\right ) y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(x),x) = (ln(y(x))+x+x^3+x^4)*y(x)/x,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {x^{4}}{3}} {\mathrm e}^{\frac {x^{3}}{2}} {\mathrm e}^{x c_{1}} x^{x} \]
✓ Solution by Mathematica
Time used: 0.321 (sec). Leaf size: 28
DSolve[y'[x] == ((x + x^3 + x^4 + Log[y[x]])*y[x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^x e^{\frac {1}{6} (2 x+3) x^3+c_1 x} \\ \end{align*}