Internal problem ID [2704]
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]
Solve \begin {gather*} \boxed {y^{\prime }+y^{2}-x^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x)+y(x)^2=1+x^2,y(x), singsol=all)
\[ y \relax (x ) = x -\frac {{\mathrm e}^{-x^{2}}}{c_{1}-\frac {\sqrt {\pi }\, \erf \relax (x )}{2}} \]
✓ Solution by Mathematica
Time used: 0.145 (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*}