Internal problem ID [3724]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 470.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (1-4 x -2 y\right ) y^{\prime }+y=-2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve((1-4*x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-2 \,{\mathrm e}^{4} {\mathrm e}^{-25 x} {\mathrm e}^{25 c_{1}}\right )+4-25 x +25 c_{1}}}{5}+\frac {2}{5}-2 x \]
✓ Solution by Mathematica
Time used: 3.953 (sec). Leaf size: 39
DSolve[(1-4 x-2 y[x])y'[x]+2 x+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{10} W\left (-e^{-25 x-1+c_1}\right )-2 x+\frac {2}{5} y(x)\to \frac {2}{5}-2 x \end{align*}