Internal problem ID [2644]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential
Equations. page 59
Problem number: Problem 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {2 y x}{x^{2}+1}=\frac {4}{\left (x^{2}+1\right )^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x)+2*x/(1+x^2)*y(x)=4/(1+x^2)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 \arctan \left (x \right )+c_{1}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 20
DSolve[y'[x]+2*x/(1+x^2)*y[x]==4/(1+x^2)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 \arctan (x)+c_1}{x^2+1} \]