62.4.3 problem Ex 3

Internal problem ID [12815]
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
Date solved : Tuesday, January 28, 2025 at 04:24:29 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +y-\left (4 x +2 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 23

dsolve((2*x+y(x))-(4*x+2*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{4-25 x +25 c_{1}}\right )}{10}+\frac {2}{5}-2 x \]

✓ Solution by Mathematica

Time used: 0.859 (sec). Leaf size: 39

DSolve[(2*x+y[x])-(4*x+2*y[x]-1)*D[y[x],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*}