Internal problem ID [8377]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 797.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 223
dsolve(diff(y(x),x) = y(x)*(-1-cosh((x+1)/(x-1))*x+cosh((x+1)/(x-1))*x^2*y(x)-cosh((x+1)/(x-1))*x^2+cosh((x+1)/(x-1))*x^3*y(x))/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\frac {{\mathrm e}^{\frac {x +1}{x -1}} x^{2}}{4}-x \,{\mathrm e}^{\frac {x +1}{x -1}}+\frac {5 \,{\mathrm e}^{\frac {x +1}{x -1}}}{4}-3 \,{\mathrm e} \expIntegral \left (1, -\frac {2}{x -1}\right )+\expIntegral \left (1, \frac {2}{x -1}\right ) {\mathrm e}^{-1}-\frac {{\mathrm e}^{-\frac {x +1}{x -1}} x^{2}}{4}+\frac {{\mathrm e}^{-\frac {x +1}{x -1}}}{4}}}{x \left (c_{1}+\int -{\mathrm e}^{-\frac {{\mathrm e}^{\frac {x +1}{x -1}} x^{2}}{4}-x \,{\mathrm e}^{\frac {x +1}{x -1}}+\frac {5 \,{\mathrm e}^{\frac {x +1}{x -1}}}{4}-3 \,{\mathrm e} \expIntegral \left (1, -\frac {2}{x -1}\right )+\expIntegral \left (1, \frac {2}{x -1}\right ) {\mathrm e}^{-1}-\frac {{\mathrm e}^{-\frac {x +1}{x -1}} x^{2}}{4}+\frac {{\mathrm e}^{-\frac {x +1}{x -1}}}{4}} \left (x +1\right ) \cosh \left (\frac {x +1}{x -1}\right )d x \right )} \]
✓ Solution by Mathematica
Time used: 2.623 (sec). Leaf size: 95
DSolve[y'[x] == (y[x]*(-1 - x*Cosh[(1 + x)/(-1 + x)] - x^2*Cosh[(1 + x)/(-1 + x)] + x^2*Cosh[(1 + x)/(-1 + x)]*y[x] + x^3*Cosh[(1 + x)/(-1 + x)]*y[x]))/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x+c_1 x \exp \left (\frac {4 \left (1-3 e^2\right ) \text {Chi}\left (\frac {2}{x-1}\right )+4 \left (1+3 e^2\right ) \text {Shi}\left (\frac {2}{1-x}\right )+e^{-\frac {2}{x-1}} (x-1) \left (x+e^{\frac {4}{x-1}+2} (x+5)+1\right )}{4 e}\right )} \\ y(x)\to 0 \\ \end{align*}