Internal problem ID [8366]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 786.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \ln \relax (x )+\cosh \relax (x ) x a y^{2}+\cosh \relax (x ) x^{3} b}{x \ln \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (y(x)*ln(x)+cosh(x)*x*a*y(x)^2+cosh(x)*x^3*b)/x/ln(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\left (\int \frac {x \cosh \relax (x )}{\ln \relax (x )}d x \right ) \sqrt {b a}+c_{1} \sqrt {b a}\right ) x \sqrt {b a}}{a} \]
✓ Solution by Mathematica
Time used: 5.822 (sec). Leaf size: 50
DSolve[y'[x] == (b*x^3*Cosh[x] + Log[x]*y[x] + a*x*Cosh[x]*y[x]^2)/(x*Log[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {b} x \tan \left (\sqrt {a} \sqrt {b} \left (\int _1^x\frac {\cosh (K[1]) K[1]}{\log (K[1])}dK[1]+c_1\right )\right )}{\sqrt {a}} \\ \end{align*}