Internal problem ID [11453]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.3.1 Nonhomogeneous Equations:
Undetermined Coefficients. Exercises page 110
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x^{\prime }+x=3 \cos \left (t \right )-2 \sin \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(x(t),t$2)+diff(x(t),t)+x(t)=3*cos(t)-2*sin(t),x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right ) c_{2} +{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) c_{1} +3 \sin \left (t \right )+2 \cos \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 56
DSolve[x''[t]+x'[t]+x[t]==3*Cos[t]-2*Sin[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to 3 \sin (t)+2 \cos (t)+c_2 e^{-t/2} \cos \left (\frac {\sqrt {3} t}{2}\right )+c_1 e^{-t/2} \sin \left (\frac {\sqrt {3} t}{2}\right ) \]