81.3.34 problem 34

Internal problem ID [18652]
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 : 34
Date solved : Tuesday, January 28, 2025 at 12:08:47 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=10 x -4 y+6 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 21

dsolve((5*x-2*y(x)+7)*diff(y(x),x)=10*x-4*y(x)+6,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {5 x}{2}+8 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {x}{16}-\frac {23}{16}}}{16}\right )+\frac {23}{2} \]

✓ Solution by Mathematica

Time used: 3.209 (sec). Leaf size: 43

DSolve[(5*x-2*y[x]+7)*D[y[x],x]==10*x-4*y[x]+6,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 8 W\left (-e^{-\frac {x}{16}-1+c_1}\right )+\frac {5 x}{2}+\frac {23}{2} \\ y(x)\to \frac {1}{2} (5 x+23) \\ \end{align*}