Internal problem ID [8290]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 710.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-\ln \relax (x )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 y^{2} x +2 x^{3}}{\ln \relax (x )-{\mathrm e}^{\frac {1}{x}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 35
dsolve(diff(y(x),x) = (-ln(x)+exp(1/x)+4*x^2*y(x)+2*x+2*x*y(x)^2+2*x^3)/(ln(x)-exp(1/x)),y(x), singsol=all)
\[ y \relax (x ) = -x +\tan \left (2 c_{1}-2 \left (\int \frac {1}{-\frac {\ln \relax (x )}{x}+\frac {{\mathrm e}^{\frac {1}{x}}}{x}}d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 1.69 (sec). Leaf size: 38
DSolve[y'[x] == (E^x^(-1) + 2*x + 2*x^3 - Log[x] + 4*x^2*y[x] + 2*x*y[x]^2)/(-E^x^(-1) + Log[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\tan \left (\int _1^x-\frac {2 K[5]}{e^{\frac {1}{K[5]}}-\log (K[5])}dK[5]+c_1\right ) \\ \end{align*}