Internal problem ID [9069]
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)]`]]
\[ \boxed {y^{\prime }-\frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 33
dsolve(diff(y(x),x) = (-ln(y(x))*x-ln(y(x))+x^3)*y(x)/(x+1),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x^{2}-3 x +4+{\mathrm e}^{-x} c_{1} +\operatorname {expIntegral}_{1}\left (-x -1\right ) {\mathrm e}^{-x -1}} \]
✓ Solution by Mathematica
Time used: 0.684 (sec). Leaf size: 37
DSolve[y'[x] == ((x^3 - Log[y[x]] - x*Log[y[x]])*y[x])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \exp \left (-e^{-x-1} \operatorname {ExpIntegralEi}(x+1)+x^2-3 x-c_1 e^{-x}+4\right ) \]