Internal problem ID [8364]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 784.
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 {-\sinh \relax (x )+x^{2} \ln \relax (x )+2 \ln \relax (x ) y x +\ln \relax (x )+y^{2} \ln \relax (x )}{\sinh \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 24
dsolve(diff(y(x),x) = (-sinh(x)+x^2*ln(x)+2*y(x)*ln(x)*x+ln(x)+y(x)^2*ln(x))/sinh(x),y(x), singsol=all)
\[ y \relax (x ) = -x -\tan \left (c_{1}-\left (\int \frac {\ln \relax (x )}{\sinh \relax (x )}d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 28.757 (sec). Leaf size: 27
DSolve[y'[x] == Csch[x]*(Log[x] + x^2*Log[x] - Sinh[x] + 2*x*Log[x]*y[x] + Log[x]*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\tan \left (\int _1^x\text {csch}(K[5]) \log (K[5])dK[5]+c_1\right ) \\ \end{align*}