29.16.1 problem 444

Internal problem ID [5042]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 444
Date solved : Monday, January 27, 2025 at 10:05:23 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3-x -y\right ) y^{\prime }&=1+x -3 y \end{align*}

✓ Solution by Maple

Time used: 0.552 (sec). Leaf size: 30

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

\[ y \left (x \right ) = \frac {\left (x -1\right ) \operatorname {LambertW}\left (-2 c_{1} \left (x -2\right )\right )+2 x -4}{\operatorname {LambertW}\left (-2 c_{1} \left (x -2\right )\right )} \]

✓ Solution by Mathematica

Time used: 1.051 (sec). Leaf size: 159

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

\[ \text {Solve}\left [\frac {2^{2/3} \left (x \left (-\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )\right )+(x-1) \log \left (\frac {6\ 2^{2/3} (x-2)}{y(x)+x-3}\right )+\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )+y(x) \left (-\log \left (\frac {6\ 2^{2/3} (x-2)}{y(x)+x-3}\right )+\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )-1\right )-x+3\right )}{9 (-y(x)+x-1)}=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ] \]