29.16.4 problem 447

Internal problem ID [5045]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 447
Date solved : Monday, January 27, 2025 at 10:05:33 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 21

dsolve((2+2*x-y(x))*diff(y(x),x)+3+6*x-3*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = 2 x -\frac {3 \operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{\frac {25 x}{3}+\frac {7}{3}}}{3}\right )}{5}+\frac {7}{5} \]

✓ Solution by Mathematica

Time used: 3.194 (sec). Leaf size: 41

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

\begin{align*} y(x)\to -\frac {3}{5} W\left (-e^{\frac {25 x}{3}-1+c_1}\right )+2 x+\frac {7}{5} \\ y(x)\to 2 x+\frac {7}{5} \\ \end{align*}