29.16.2 problem 445

Internal problem ID [5043]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 445
Date solved : Monday, January 27, 2025 at 10:05:26 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \end{align*}

✓ Solution by Maple

Time used: 0.543 (sec). Leaf size: 30

dsolve((3-x+y(x))*diff(y(x),x) = 11-4*x+3*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (2 x -5\right ) \operatorname {LambertW}\left (-c_{1} \left (x -2\right )\right )+x -2}{\operatorname {LambertW}\left (-c_{1} \left (x -2\right )\right )} \]

✓ Solution by Mathematica

Time used: 1.308 (sec). Leaf size: 179

DSolve[(3-x+y[x])D[y[x],x]==11-4 x+3 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {(-2)^{2/3} \left (-2 x \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+(2 x-5) \log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+5 \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+y(x) \left (-\log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+\log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )-1\right )+x-3\right )}{9 (-y(x)+2 x-5)}=\frac {1}{9} (-2)^{2/3} \log (x-2)+c_1,y(x)\right ] \]