Internal problem ID [8327]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 747.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y \left (\tan \relax (x )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 69
dsolve(diff(y(x),x) = -y(x)*(tan(x)+ln(2*x)*x-ln(2*x)*x^2*y(x))/x/tan(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{\int -\frac {x \ln \relax (x )+x \ln \relax (2)+\tan \relax (x )}{x \tan \relax (x )}d x}}{\int -\frac {{\mathrm e}^{\int -\frac {x \ln \relax (x )+x \ln \relax (2)+\tan \relax (x )}{x \tan \relax (x )}d x} \left (\ln \relax (2)+\ln \relax (x )\right ) x}{\tan \relax (x )}d x +c_{1}} \]
✓ Solution by Mathematica
Time used: 4.051 (sec). Leaf size: 89
DSolve[y'[x] == -((Cot[x]*y[x]*(x*Log[2*x] + Tan[x] - x^2*Log[2*x]*y[x]))/x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\exp \left (\int _1^x\left (-\cot (K[1]) \log (2 K[1])-\frac {1}{K[1]}\right )dK[1]\right )}{-\int _1^x\exp \left (\int _1^{K[2]}\left (-\cot (K[1]) \log (2 K[1])-\frac {1}{K[1]}\right )dK[1]\right ) \cot (K[2]) K[2] \log (2 K[2])dK[2]+c_1} \\ y(x)\to 0 \\ \end{align*}