Internal problem ID [1940]
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: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-2 y+\left (1-x +2 y\right ) y^{\prime }=-x -3} \] With initial conditions \begin {align*} [y \left (-4\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 20
dsolve([(x-2*y(x)+3)+(1-x+2*y(x))*diff(y(x),x)=0,y(-4) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {7}{2}+\frac {x}{2}+4 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {x}{8}+\frac {5}{8}}}{8}\right ) \]
✓ Solution by Mathematica
Time used: 4.645 (sec). Leaf size: 28
DSolve[{(x-2*y[x]+3)+(1-x+2*y[x])*y'[x]==0,{y[-4]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (8 W\left (\frac {1}{8} e^{\frac {x+5}{8}}\right )+x+7\right ) \]