29.17.12 problem 471

Internal problem ID [5069]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 471
Date solved : Monday, January 27, 2025 at 10:07:35 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 23

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

\[ y \left (x \right ) = -\frac {2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{2}\right )}{5}+3 x -\frac {2}{5} \]

✓ Solution by Mathematica

Time used: 3.210 (sec). Leaf size: 40

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

\begin{align*} y(x)\to 3 x-\frac {2}{5} \left (1+W\left (-e^{\frac {25 x}{4}-1+c_1}\right )\right ) \\ y(x)\to 3 x-\frac {2}{5} \\ \end{align*}