28.1.68 problem 71.1

Internal problem ID [4374]
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
Date solved : Monday, January 27, 2025 at 09:09:29 AM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }+y^{2}&=x^{2}+1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.137 (sec). Leaf size: 36

DSolve[D[y[x],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*}