7.5.64 problem 65

Internal problem ID [168]
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 : 65
Date solved : Friday, February 07, 2025 at 08:00:09 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

\[ y = \frac {c_1 x +x^{2}-1}{x +c_1} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 20

DSolve[D[y[x],x]+2*x*y[x]==1+x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x+\frac {1}{-x+c_1} \\ y(x)\to x \\ \end{align*}