Internal problem ID [3216]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 471.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (-2 y+6 x \right ) y^{\prime }-2-3 x +y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve((6*x-2*y(x))*diff(y(x),x) = 2+3*x-y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{4}} {\mathrm e}^{-1} {\mathrm e}^{-\frac {25 c_{1}}{4}}}{2}\right )+\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{5}+3 x -\frac {2}{5} \]
✓ Solution by Mathematica
Time used: 3.845 (sec). Leaf size: 40
DSolve[(6 x-2 y[x])y'[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*}