Internal problem ID [5036]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _exact, _dAlembert]
Solve \begin {gather*} \boxed {\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right )-\frac {x +y}{x +3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.625 (sec). Leaf size: 27
dsolve((diff(y(x),x)+1)*ln((y(x)+x)/(x+3))=(y(x)+x)/(x+3),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\LambertW \left (\frac {{\mathrm e}^{-1}}{\left (3+x \right ) c_{1}}\right )+1} \left (3+x \right )-x \]
✓ Solution by Mathematica
Time used: 0.409 (sec). Leaf size: 30
DSolve[(y'[x]+1)*Log[(y[x]+x)/(x+3)]==(y[x]+x)/(x+3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-y(x)+(y(x)+x) \log \left (\frac {y(x)+x}{x+3}\right )-x=c_1,y(x)\right ] \]