Internal problem ID [3216]
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]]
Solve \begin {gather*} \boxed {\left (1-4 x -2 y\right ) y^{\prime }+2 x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 35
dsolve((1-4*x-2*y(x))*diff(y(x),x)+2*x+y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\LambertW \left (-2 \,{\mathrm e}^{4} {\mathrm e}^{-25 x} {\mathrm e}^{25 c_{1}}\right )+4-25 x +25 c_{1}}}{5}+\frac {2}{5}-2 x \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 28
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} \text {ProductLog}\left (-e^{-25 x-1+c_1}\right )-2 x+\frac {2}{5} \\ \end{align*}