Internal problem ID [3710]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 456.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (a +b x +y\right ) y^{\prime }-y=b x -a} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 91
dsolve((a+b*x+y(x))*diff(y(x),x)+a-b*x-y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-b^{2} x +2 \operatorname {LambertW}\left (\frac {{\mathrm e}^{-\frac {c_{1} b^{2}}{2 a}} {\mathrm e}^{\frac {b^{2} x}{2 a}} {\mathrm e}^{-\frac {c_{1} b}{a}} {\mathrm e}^{\frac {b}{2}} {\mathrm e}^{\frac {x b}{a}} {\mathrm e}^{-\frac {c_{1}}{2 a}} {\mathrm e}^{-\frac {1}{2}} {\mathrm e}^{\frac {x}{2 a}}}{2 a}\right ) a -a b -x b +a}{b +1} \]
✓ Solution by Mathematica
Time used: 5.745 (sec). Leaf size: 118
DSolve[(a+b x+y[x])y'[x]+a-b x-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 a W\left (-e^{\frac {(b+1)^2 x}{2 a}-1+c_1}\right )+a (-b)+a-b (b+1) x}{b+1} y(x)\to \frac {a (-b)+a-b (b+1) x}{b+1} y(x)\to \frac {2 a W\left (-e^{\frac {(b+1)^2 x}{2 a}-1}\right )+a (-b)+a-b (b+1) x}{b+1} \end{align*}