Internal problem ID [11683]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {T^{\prime }+k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(T(t),t)=-k*(T(t)- (mu+a*cos( omega*(t-phi)))),T(t), singsol=all)
\[ T \left (t \right ) = {\mathrm e}^{-k t} c_{1} -\frac {\sin \left (\omega \left (-t +\phi \right )\right ) a k \omega -\cos \left (\omega \left (-t +\phi \right )\right ) a \,k^{2}-k^{2} \mu -\mu \,\omega ^{2}}{k^{2}+\omega ^{2}} \]
✓ Solution by Mathematica
Time used: 0.511 (sec). Leaf size: 60
DSolve[T'[t]==-k*(T[t]- (mu+a*Cos[ omega*(t-phi)])),T[t],t,IncludeSingularSolutions -> True]
\[ T(t)\to -\frac {a k \omega \sin (\omega (\phi -t))}{k^2+\omega ^2}+\frac {a k^2 \cos (\omega (\phi -t))}{k^2+\omega ^2}+c_1 e^{-k t}+\mu \]