Internal problem ID [14542]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=-78 \cos \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(t),t$2)-5*diff(y(t),t)+6*y(t)=-78*cos(3*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{2 t}+5 \sin \left (3 t \right )+\cos \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 31
DSolve[y''[t]-5*y'[t]+6*y[t]==-78*Cos[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 5 \sin (3 t)+\cos (3 t)+e^{2 t} \left (c_2 e^t+c_1\right ) \]