Internal problem ID [10125]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 11. Equations
in which M and N are linear but not homogeneous. Page 16
Problem number: Ex 3.
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 {2 x +y-\left (4 x +2 y-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve((2*x+y(x))-(4*x+2*y(x)-1)*diff(y(x),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: 60.023 (sec). Leaf size: 28
DSolve[(2*x+y[x])-(4*x+2*y[x]-1)*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*}