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: 0.063 (sec). Leaf size: 63
dsolve((a+b*x+y(x))*diff(y(x),x)+a-b*x-y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {-c_{1} \left (b +1\right )^{2}+\left (b -1\right ) a +x \left (b +1\right )^{2}}{2 a}}}{2 a}\right ) a -b^{2} x +\left (-a -x \right ) b +a}{b +1} \]
✓ 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*}