Internal problem ID [1936]
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: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y-\left (2 x +2 y-1\right ) y^{\prime }=-x -4} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 20
dsolve([(x+y(x)+4)=(2*x+2*y(x)-1)*diff(y(x),x),y(0) = 0],y(x), singsol=all)
\[ y = -x -\frac {3 \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-x -\frac {2}{3}}}{3}\right )}{2}-1 \]
✓ Solution by Mathematica
Time used: 3.156 (sec). Leaf size: 28
DSolve[{(x+y[x]+4)==(2*x+2*y[x]-1)*y'[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {3}{2} W\left (-\frac {2}{3} e^{-x-\frac {2}{3}}\right )-x-1 \]