Internal problem ID [8363]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 785.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
\[ \boxed {y^{\prime }+\frac {\ln \left (x \right )-x^{2} \sinh \left (x \right )-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x) = -(ln(x)-sinh(x)*x^2-2*sinh(x)*x*y(x)-sinh(x)-sinh(x)*y(x)^2)/ln(x),y(x), singsol=all)
\[ y \left (x \right ) = -x -\tan \left (c_{1} -\left (\int \frac {\sinh \left (x \right )}{\ln \left (x \right )}d x \right )\right ) \]
✓ Solution by Mathematica
Time used: 11.335 (sec). Leaf size: 29
DSolve[y'[x] == (-Log[x] + Sinh[x] + x^2*Sinh[x] + 2*x*Sinh[x]*y[x] + Sinh[x]*y[x]^2)/Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x+\tan \left (\int _1^x\frac {\sinh (K[5])}{\log (K[5])}dK[5]+c_1\right ) \\ \end{align*}