19.2.5 problem 5

Internal problem ID [3534]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 5
Date solved : Monday, January 27, 2025 at 07:40:55 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.000 (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: 0.037 (sec). Leaf size: 20

DSolve[D[y[x],x]+2*x/(1+x^2)*y[x]==4/(1+x^2)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 \arctan (x)+c_1}{x^2+1} \]