81.3.33 problem 33

Internal problem ID [18651]
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 : 33
Date solved : Tuesday, January 28, 2025 at 12:08:45 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 21

dsolve((x-3*y(x)+4)*diff(y(x),x)=2*x-6*y(x)+7,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x}{3}-\frac {\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {17}{3}-\frac {25 x}{3}}}{3}\right )}{5}+\frac {17}{15} \]

✓ Solution by Mathematica

Time used: 4.039 (sec). Leaf size: 43

DSolve[(x-3*y[x]+4)*D[y[x],x]==2*x-6*y[x]+7,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{15} \left (-3 W\left (-e^{-\frac {25 x}{3}-1+c_1}\right )+5 x+17\right ) \\ y(x)\to \frac {1}{15} (5 x+17) \\ \end{align*}