Internal problem ID [6077]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
190
Problem number: 5(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {y+x +1}{2 x +2 y-1}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(x),x)=(x+y(x)+1)/(2*x+2*y(x)-1),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-3 x} {\mathrm e}^{3 c_{1}}\right )-3 x +3 c_{1}}-x \]
✓ Solution by Mathematica
Time used: 4.2 (sec). Leaf size: 32
DSolve[y'[x]==(x+y[x]+1)/(2*x+2*y[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x-\frac {1}{2} W\left (-e^{-3 x-1+c_1}\right ) y(x)\to -x \end{align*}