75.12.1 problem 275

Internal problem ID [16867]
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
Date solved : Tuesday, January 28, 2025 at 09:35:57 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (x -y\right )^{2}+1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve(diff(y(x),x)=(x-y(x))^2+1,y(x), singsol=all)
 

\[ y = \frac {c_{1} x +x^{2}-1}{x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 20

DSolve[D[y[x],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*}