Internal problem ID [2082]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 53.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-2 y-\left (x -2 y+1\right ) y^{\prime }=-3-x} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 20
dsolve([(x-2*y(x)+3)=(x-2*y(x)+1)*diff(y(x),x),y(0) = 2],y(x), singsol=all)
\[ y = \frac {5}{2}+\frac {x}{2}+2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {x}{4}-\frac {1}{4}}}{4}\right ) \]
✓ Solution by Mathematica
Time used: 4.657 (sec). Leaf size: 28
DSolve[{(x-2*y[x]+3)==(x-2*y[x]+1)*y'[x],{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (4 W\left (-\frac {1}{4} e^{\frac {x-1}{4}}\right )+x+5\right ) \]