7.5.63 problem 64

Internal problem ID [167]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 64
Date solved : Friday, February 07, 2025 at 08:00:07 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

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

\[ y = \frac {\operatorname {erf}\left (x \right ) \sqrt {\pi }\, x -2 c_1 x +2 \,{\mathrm e}^{-x^{2}}}{\sqrt {\pi }\, \operatorname {erf}\left (x \right )-2 c_1} \]

✓ Solution by Mathematica

Time used: 0.121 (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*}