Internal problem ID [1922]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-\tanh \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.334 (sec). Leaf size: 113
dsolve(diff(y(x),x)=y(x)/x+tanh(y(x)/x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \arctanh \left (\frac {c_{1} x^{2}-\sqrt {c_{1}^{2} x^{4}-c_{1} x^{2}}}{c_{1} x^{2}-1-\sqrt {c_{1}^{2} x^{4}-c_{1} x^{2}}}\right ) x \\ y \relax (x ) = \arctanh \left (\frac {c_{1} x^{2}+\sqrt {c_{1}^{2} x^{4}-c_{1} x^{2}}}{c_{1} x^{2}-1+\sqrt {c_{1}^{2} x^{4}-c_{1} x^{2}}}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.462 (sec). Leaf size: 19
DSolve[y'[x]==y[x]/x+Tanh[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sinh ^{-1}\left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}