29.8.13 problem 218

Internal problem ID [4818]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 218
Date solved : Monday, January 27, 2025 at 09:41:15 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=y-2 x \tanh \left (\frac {y}{x}\right ) \end{align*}

✓ Solution by Maple

Time used: 1.493 (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 \left (x \right ) &= \operatorname {arctanh}\left (\frac {1}{\sqrt {-c_{1} x^{4}+1}}\right ) x \\ y \left (x \right ) &= -\operatorname {arctanh}\left (\frac {1}{\sqrt {-c_{1} x^{4}+1}}\right ) x \\ \end{align*}

✓ Solution by Mathematica

Time used: 10.732 (sec). Leaf size: 21

DSolve[x D[y[x],x]==y[x]-2 x Tanh[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \text {arcsinh}\left (\frac {e^{c_1}}{x^2}\right ) \\ y(x)\to 0 \\ \end{align*}