Internal problem ID [2966]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 218.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y+2 \tanh \left (\frac {y}{x}\right ) x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.268 (sec). Leaf size: 34
dsolve(x*diff(y(x),x) = y(x)-2*x*tanh(y(x)/x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \arctanh \left (\frac {1}{\sqrt {-c_{1} x^{4}+1}}\right ) x \\ y \relax (x ) = -\arctanh \left (\frac {1}{\sqrt {-c_{1} x^{4}+1}}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.068 (sec). Leaf size: 21
DSolve[x y'[x]==y[x]-2 x Tanh[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sinh ^{-1}\left (\frac {e^{c_1}}{x^2}\right ) \\ y(x)\to 0 \\ \end{align*}