Internal problem ID [11149]
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`]]
\[ \boxed {y-\left (4 x +2 y-1\right ) y^{\prime }=-2 x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 35
dsolve((2*x+y(x))-(4*x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-2 \,{\mathrm e}^{4} {\mathrm e}^{-25 x} {\mathrm e}^{25 c_{1}}\right )+4-25 x +25 c_{1}}}{5}+\frac {2}{5}-2 x \]
✓ Solution by Mathematica
Time used: 4.725 (sec). Leaf size: 39
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} W\left (-e^{-25 x-1+c_1}\right )-2 x+\frac {2}{5} y(x)\to \frac {2}{5}-2 x \end{align*}