Internal problem ID [13206]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.2 page 412
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y=-4 \cos \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=-4*cos(3*t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{-4 t} c_{1}}{2}+c_{2} {\mathrm e}^{-2 t}+\frac {4 \cos \left (3 t \right )}{325}-\frac {72 \sin \left (3 t \right )}{325} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 37
DSolve[y''[t]+6*y'[t]+8*y[t]==-4*Cos[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_1 e^{-4 t}+c_2 e^{-2 t}+\frac {4}{325} (\cos (3 t)-18 \sin (3 t)) \]