65.4.9 problem 9.4

Internal problem ID [13739]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 9, First order linear equations and the integrating factor. Exercises page 86
Problem number : 9.4
Date solved : Tuesday, January 28, 2025 at 06:00:22 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} T^{\prime }&=-k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 58

dsolve(diff(T(t),t)=-k*(T(t)- (mu+a*cos( omega*(t-phi)))),T(t), singsol=all)
 

\[ T = \frac {\cos \left (\omega \left (-t +\phi \right )\right ) a \,k^{2}-\sin \left (\omega \left (-t +\phi \right )\right ) a k \omega +\left (k^{2}+\omega ^{2}\right ) \left ({\mathrm e}^{-k t} c_{1} +\mu \right )}{k^{2}+\omega ^{2}} \]

✓ Solution by Mathematica

Time used: 0.704 (sec). Leaf size: 74

DSolve[D[ T[t],t]==-k*(T[t]- (mu+a*Cos[ omega*(t-phi)])),T[t],t,IncludeSingularSolutions -> True]
 

\[ T(t)\to \frac {a k e^{-i \omega (\phi +t)} \left ((k+i \omega ) e^{2 i \omega \phi }+(k-i \omega ) e^{2 i \omega t}\right )}{2 \left (k^2+\omega ^2\right )}+c_1 e^{-k t}+\mu \]