81.3.35 problem 35

Internal problem ID [18653]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 12:08:49 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 x -2 y+5\right ) y^{\prime }&=x -y+3 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 19

dsolve((2*x-2*y(x)+5)*diff(y(x),x)=x-y(x)+3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.049 (sec). Leaf size: 29

DSolve[(2*x-2*y[x]+5)*D[y[x],x]==x-y[x]+3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} W\left (-e^{x-1+c_1}\right )+x+2 \\ y(x)\to x+2 \\ \end{align*}