Internal problem ID [1926]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y+\left (x +y-1\right ) y^{\prime }=-x -2} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve((x-y(x)+2)+(x+y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {3}{2}-\frac {\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (2 x +1\right )+2 c_{1} \right )\right ) \left (2 x +1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 63
DSolve[(x-y[x]+2)+(x+y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)-x-2}{y(x)+x-1}\right )+\log \left (\frac {2 x^2+2 y(x)^2-6 y(x)+2 x+5}{(2 x+1)^2}\right )+2 \log (2 x+1)+c_1=0,y(x)\right ] \]