76.2.4 problem 4

Internal problem ID [17340]
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 : 4
Date solved : Tuesday, January 28, 2025 at 10:01:44 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{t}&=5+\cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

dsolve(diff(y(t),t)+(1/t)*y(t)=5+cos(2*t),y(t), singsol=all)
 

\[ y = \frac {10 t^{2}+4 c_{1} +2 \sin \left (2 t \right ) t +\cos \left (2 t \right )}{4 t} \]

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 29

DSolve[D[y[t],t]+(1/t)*y[t]==5+Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\int _1^t(\cos (2 K[1])+5) K[1]dK[1]+c_1}{t} \]