Internal problem ID [8561]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 225.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (4 y+2 x +3\right ) y^{\prime }-2 y=x +1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve((4*y(x)+2*x+3)*diff(y(x),x)-2*y(x)-x-1=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{2}+\frac {\operatorname {LambertW}\left ({\mathrm e}^{5} {\mathrm e}^{8 x} c_{1} \right )}{8}-\frac {5}{8} \]
✓ Solution by Mathematica
Time used: 4.688 (sec). Leaf size: 39
DSolve[(4*y[x]+2*x+3)*y'[x]-2*y[x]-x-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{8} \left (W\left (-e^{8 x-1+c_1}\right )-4 x-5\right ) y(x)\to \frac {1}{8} (-4 x-5) \end{align*}