Internal problem ID [2135]
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]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 x y}{x^{2}+1}-\frac {4}{\left (x^{2}+1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (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)
\[ y \relax (x ) = \frac {4 \arctan \relax (x )+c_{1}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 20
DSolve[y'[x]+2*x/(1+x^2)*y[x]==4/(1+x^2)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 \text {ArcTan}(x)+c_1}{x^2+1} \\ \end{align*}