Internal problem ID [5276]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 24 (L).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y-\left (-y+x -3\right ) y^{\prime }=-1-x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve((x+y(x)+1)-(x-y(x)-3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -2-\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x -1\right )+2 c_{1} \right )\right ) \left (x -1\right ) \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 58
DSolve[(x+y[x]+1)-(x-y[x]-3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)+x+1}{y(x)-x+3}\right )+\log \left (\frac {x^2+y(x)^2+4 y(x)-2 x+5}{2 (x-1)^2}\right )+2 \log (x-1)+c_1=0,y(x)\right ] \]