10.1.8 problem 8

Internal problem ID [1105]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 8
Date solved : Monday, January 27, 2025 at 04:33:36 AM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

\[ y = \frac {\arctan \left (t \right )+c_1}{\left (t^{2}+1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 18

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

\[ y(t)\to \frac {\arctan (t)+c_1}{\left (t^2+1\right )^2} \]