Internal problem ID [2488]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 10.
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 {2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \left (-2\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 20
dsolve([(2*x+3*y(x)+1)+(4*x+6*y(x)+1)*diff(y(x),x)=0,y(-2) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{3}-\frac {2 x}{3}+\frac {\LambertW \left (\frac {2 \,{\mathrm e}^{\frac {x}{3}+\frac {4}{3}}}{3}\right )}{2} \]
✓ Solution by Mathematica
Time used: 60.028 (sec). Leaf size: 30
DSolve[{(2*x+3*y[x]+1)+(4*x+6*y[x]+1)*y'[x]==0,y[-2]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (3 \text {ProductLog}\left (\frac {2}{3} e^{\frac {x+4}{3}}\right )-4 x+2\right ) \\ \end{align*}