Internal problem ID [3225]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 479.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (4-x -3 y\right ) y^{\prime }+3-x -3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve((4-x-3*y(x))*diff(y(x),x)+3-x-3*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{3}-\frac {\LambertW \left (-\frac {{\mathrm e}^{\frac {4 x}{3}} {\mathrm e}^{\frac {5}{3}} c_{1}}{3}\right )}{2}+\frac {5}{6} \]
✓ Solution by Mathematica
Time used: 60.026 (sec). Leaf size: 30
DSolve[(4-x-3 y[x])y'[x]+3-x-3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (-3 \text {ProductLog}\left (-e^{\frac {4 x}{3}-1+c_1}\right )-2 x+5\right ) \\ \end{align*}