Internal problem ID [1923]
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: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y-\left (x -y+2\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve((x+y(x))-(x-y(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = 1-\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x +1\right )+2 c_{1} \right )\right ) \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 56
DSolve[(x+y[x])-(x-y[x]+2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)+x}{-y(x)+x+2}\right )=\log \left (\frac {x^2+y(x)^2-2 y(x)+2 x+2}{2 (x+1)^2}\right )+2 \log (x+1)+c_1,y(x)\right ] \]