Internal problem ID [1937]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 y+\left (2 x +3 y+2\right ) y^{\prime }=1-2 x} \] With initial conditions \begin {align*} [y \left (3\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 20
dsolve([(2*x+3*y(x)-1)+(2*x+3*y(x)+2)*diff(y(x),x)=0,y(3) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {7}{3}-\frac {2 x}{3}+3 \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {5}{9}-\frac {x}{9}}}{9}\right ) \]
✓ Solution by Mathematica
Time used: 4.691 (sec). Leaf size: 32
DSolve[{(2*x+3*y[x]-1)+(2*x+3*y[x]+2)*y'[x]==0,{y[3]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (9 W\left (\frac {2}{9} e^{\frac {5}{9}-\frac {x}{9}}\right )-2 x+7\right ) \]