Internal problem ID [3213]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 71.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+y^{2}=x^{2}+1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x)+y(x)^2=1+x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {\pi }\, \operatorname {erf}\left (x \right ) x -2 c_{1} x +2 \,{\mathrm e}^{-x^{2}}}{\sqrt {\pi }\, \operatorname {erf}\left (x \right )-2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 36
DSolve[y'[x]+y[x]^2==1+x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {2 e^{-x^2}}{\sqrt {\pi } \text {erf}(x)+2 c_1} \\ y(x)\to x \\ \end{align*}