Internal problem ID [3741]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 487.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {4 \left (1-x -y\right ) y^{\prime }=x -2} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 29
dsolve(4*(1-x-y(x))*diff(y(x),x)+2-x = 0,y(x), singsol=all)
\[ y \left (x \right ) = -1-\frac {\left (x -2\right ) \left (-1+\operatorname {LambertW}\left (-c_{1} \left (x -2\right )\right )\right )}{2 \operatorname {LambertW}\left (-c_{1} \left (x -2\right )\right )} \]
✓ Solution by Mathematica
Time used: 3.485 (sec). Leaf size: 109
DSolve[4(1-x-y[x])y'[x]+2-x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2^{2/3} \left (x \log \left (\frac {x-2}{y(x)+x-1}\right )-x \log \left (\frac {2 y(x)+x}{y(x)+x-1}\right )+2 y(x) \left (\log \left (\frac {x-2}{y(x)+x-1}\right )-\log \left (\frac {2 y(x)+x}{y(x)+x-1}\right )+1\right )+2 x-2\right )}{9 (2 y(x)+x)}=\frac {1}{9} 2^{2/3} \log (x-2)+c_1,y(x)\right ] \]