Internal problem ID [15137]
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: 275.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }-\left (-y+x \right )^{2}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x)=(x-y(x))^2+1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x +x^{2}-1}{x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 20
DSolve[y'[x]==(x-y[x])^2+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {1}{-x+c_1} \\ y(x)\to x \\ \end{align*}