18.5 problem 481

Internal problem ID [3227]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 18
Problem number: 481.
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 (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y=0} \end {gather*}

Solution by Maple

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

dsolve((5-2*x-3*y(x))*diff(y(x),x)+1-2*x-3*y(x) = 0,y(x), singsol=all)
 

\[ y \relax (x ) = -\frac {2 x}{3}-4 \LambertW \left (-\frac {{\mathrm e}^{\frac {x}{12}} c_{1} {\mathrm e}^{-\frac {7}{12}}}{12}\right )-\frac {7}{3} \]

Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

DSolve[(5-2 x-3 y[x])y'[x]+1-2 x -3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -4 \text {ProductLog}\left (-e^{\frac {x}{12}-1+c_1}\right )-\frac {2 x}{3}-\frac {7}{3} \\ \end{align*}