Internal problem ID [3698]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 444.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (3-x -y\right ) y^{\prime }+3 y=x +1} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 28
dsolve((3-x-y(x))*diff(y(x),x) = 1+x-3*y(x),y(x), singsol=all)
\[ y \left (x \right ) = 1+\frac {\left (x -2\right ) \left (\operatorname {LambertW}\left (-2 c_{1} \left (x -2\right )\right )+2\right )}{\operatorname {LambertW}\left (-2 c_{1} \left (x -2\right )\right )} \]
✓ Solution by Mathematica
Time used: 1.073 (sec). Leaf size: 159
DSolve[(3-x-y[x])y'[x]==1+x-3 y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2^{2/3} \left (x \left (-\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )\right )+(x-1) \log \left (\frac {6\ 2^{2/3} (x-2)}{y(x)+x-3}\right )+\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )+y(x) \left (-\log \left (\frac {6\ 2^{2/3} (x-2)}{y(x)+x-3}\right )+\log \left (-\frac {3\ 2^{2/3} (-y(x)+x-1)}{y(x)+x-3}\right )-1\right )-x+3\right )}{9 (-y(x)+x-1)}=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ] \]