81.3.36 problem 36

Internal problem ID [18654]
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 : 36
Date solved : Tuesday, January 28, 2025 at 12:08:51 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (6 x -4 y+1\right ) y^{\prime }&=3 x -2 y+1 \end{align*}

✓ Solution by Maple

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

dsolve((6*x-4*y(x)+1)*diff(y(x),x)=3*x-2*y(x)+1,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {3 x}{2}-\frac {\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{1+8 x}\right )}{8}+\frac {1}{8} \]

✓ Solution by Mathematica

Time used: 3.973 (sec). Leaf size: 41

DSolve[(6*x-4*y[x]+1)*D[y[x],x]==3*x-2*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (-W\left (-e^{8 x-1+c_1}\right )+12 x+1\right ) \\ y(x)\to \frac {3 x}{2}+\frac {1}{8} \\ \end{align*}