Internal problem ID [155]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Chapter 1 review problems. Page 78
Problem number: 35 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x +2 y x}{x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(x),x) = (2*x+2*x*y(x))/(x^2+1),y(x), singsol=all)
\[ y \relax (x ) = -1+\left (x^{2}+1\right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 20
DSolve[y'[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*}