Internal problem ID [8314]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 734.
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^{3}\right ) y}{x +1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.076 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (-ln(y(x))*x-ln(y(x))+x^3)*y(x)/(x+1),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x^{2}} {\mathrm e}^{-3 x} {\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{-x} c_{1}} {\mathrm e}^{{\mathrm e}^{-1} \expIntegral \left (1, -x -1\right ) {\mathrm e}^{-x}} \]
✓ Solution by Mathematica
Time used: 0.67 (sec). Leaf size: 33
DSolve[y'[x] == ((x^3 - Log[y[x]] - x*Log[y[x]])*y[x])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (-e^{-x-1} (\text {ExpIntegralEi}(x+1)+e c_1)+x^2-3 x+4\right ) \\ \end{align*}