8.6.35 problem 35 (a)

Internal problem ID [805]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 35 (a)
Date solved : Monday, January 27, 2025 at 03:08:29 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 20

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

\begin{align*} y(x)\to -1+c_1 \left (x^2+1\right ) \\ y(x)\to -1 \\ \end{align*}