17.12 problem 471

Internal problem ID [3217]

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]]

Solve \begin {gather*} \boxed {\left (-2 y+6 x \right ) y^{\prime }-2-3 x +y=0} \end {gather*}

Solution by Maple

Time used: 0.014 (sec). Leaf size: 35

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

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

Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

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+\text {ProductLog}\left (-e^{\frac {25 x}{4}-1+c_1}\right )\right ) \\ \end{align*}