Internal problem ID [15173]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 311.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational]
\[ \boxed {y^{\prime }-\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x)=2*( (y(x)+2)/(x+y(x)-1) )^2,y(x), singsol=all)
\[ y = -2+\left (-x +3\right ) \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\tan \left (\textit {\_Z} \right )\right )+\ln \left (x -3\right )+c_{1} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 27
DSolve[y'[x]==2*( (y[x]+2)/(x+y[x]-1) )^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \arctan \left (\frac {3-x}{y(x)+2}\right )+\log (y(x)+2)=c_1,y(x)\right ] \]