Internal problem ID [1922]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 6, page 25
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {y}{x}-\tanh \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.422 (sec). Leaf size: 103
dsolve(diff(y(x),x)=y(x)/x+tanh(y(x)/x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \operatorname {arctanh}\left (\frac {-c_{1} x^{2}+\sqrt {c_{1} x^{2} \left (c_{1} x^{2}-1\right )}}{-c_{1} x^{2}+\sqrt {c_{1} x^{2} \left (c_{1} x^{2}-1\right )}+1}\right ) x \\ y \left (x \right ) &= \operatorname {arctanh}\left (\frac {c_{1} x^{2}+\sqrt {c_{1} x^{2} \left (c_{1} x^{2}-1\right )}}{c_{1} x^{2}-1+\sqrt {c_{1} x^{2} \left (c_{1} x^{2}-1\right )}}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.284 (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 \text {arcsinh}\left (e^{c_1} x\right ) \\ y(x)\to 0 \\ \end{align*}