Internal problem ID [11711]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 y+\left (4 x +6 y+1\right ) y^{\prime }=-2 x -1} \] With initial conditions \begin {align*} [y \left (-2\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.156 (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)
\[ y \left (x \right ) = \frac {1}{3}-\frac {2 x}{3}+\frac {\operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {4}{3}+\frac {x}{3}}}{3}\right )}{2} \]
✓ Solution by Mathematica
Time used: 4.146 (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]
\[ y(x)\to \frac {1}{6} \left (3 W\left (\frac {2}{3} e^{\frac {x+4}{3}}\right )-4 x+2\right ) \]