Internal problem ID [3191]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 445.
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 (3-x +y\right ) y^{\prime }-11+4 x -3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.422 (sec). Leaf size: 30
dsolve((3-x+y(x))*diff(y(x),x) = 11-4*x+3*y(x),y(x), singsol=all)
\[ y \relax (x ) = -1+\frac {\left (x -2\right ) \left (2 \LambertW \left (-c_{1} \left (x -2\right )\right )+1\right )}{\LambertW \left (-c_{1} \left (x -2\right )\right )} \]
✓ Solution by Mathematica
Time used: 1.361 (sec). Leaf size: 179
DSolve[(3-x+y[x])y'[x]==11-4 x+3 y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {(-2)^{2/3} \left (-2 x \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+(2 x-5) \log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+5 \log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )+y(x) \left (-\log \left (-\frac {3 (-2)^{2/3} (x-2)}{-y(x)+x-3}\right )+\log \left (\frac {3 (-2)^{2/3} (-y(x)+2 x-5)}{-y(x)+x-3}\right )-1\right )+x-3\right )}{9 (-y(x)+2 x-5)}=\frac {1}{9} (-2)^{2/3} \log (x-2)+c_1,y(x)\right ] \]