Internal problem ID [512]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 35.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +3 y}{x -y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x) = (x+3*y(x))/(x-y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (\LambertW \left (-2 x c_{1}\right )+2\right )}{\LambertW \left (-2 x c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 33
DSolve[y'[x] == (x+3*y[x])/(x-y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{\frac {y(x)}{x}+1}+\log \left (\frac {y(x)}{x}+1\right )=-\log (x)+c_1,y(x)\right ] \]