Internal problem ID [2651]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 15.
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 (3+2 x +4 y\right ) y^{\prime }-x -2 y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((3+2*x+4*y(x))*diff(y(x),x)=1+x+2*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{2}+\frac {\LambertW \left ({\mathrm e}^{5} {\mathrm e}^{8 x} c_{1}\right )}{8}-\frac {5}{8} \]
✓ Solution by Mathematica
Time used: 60.021 (sec). Leaf size: 26
DSolve[(3+2*x+4*y[x])*y'[x]==1+x+2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (\text {ProductLog}\left (-e^{8 x-1+c_1}\right )-4 x-5\right ) \\ \end{align*}