29.8.9 problem 214

Internal problem ID [4814]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 214
Date solved : Monday, January 27, 2025 at 09:40:55 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=x +y+x \,{\mathrm e}^{\frac {y}{x}} \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 20

dsolve(x*diff(y(x),x) = x+y(x)+x*exp(y(x)/x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (\ln \left (-\frac {x}{x \,{\mathrm e}^{c_{1}}-1}\right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 4.404 (sec). Leaf size: 38

DSolve[x D[y[x],x]==x+y[x]+x Exp[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \log \left (\frac {1}{2} \left (-1+\tanh \left (\frac {1}{2} (-\log (x)-c_1)\right )\right )\right ) \\ y(x)\to i \pi x \\ \end{align*}