76.2.8 problem 8

Internal problem ID [17344]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 10:01:52 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve((1+t^2)*diff(y(t),t)+4*t*y(t)=1/(1+t^2)^2,y(t), singsol=all)
 

\[ y = \frac {\arctan \left (t \right )+c_{1}}{\left (t^{2}+1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 31

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

\[ y(t)\to \frac {\int _1^t\frac {1}{K[1]^2+1}dK[1]+c_1}{\left (t^2+1\right )^2} \]