Internal problem ID [8331]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 751.
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 +\ln \relax (y)+x^{4}\right ) y}{x \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 26
dsolve(diff(y(x),x) = (ln(y(x))*x+ln(y(x))+x^4)*y(x)/x/(x+1),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {x^{3}}{2}} \left (x +1\right )^{x} {\mathrm e}^{c_{1} x} {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.46 (sec). Leaf size: 28
DSolve[y'[x] == ((x^4 + Log[y[x]] + x*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+1)^x e^{\frac {1}{2} (x-2) x^2+c_1 x} \\ \end{align*}