Internal problem ID [14848]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+5 y=3 \sin \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=3*sin(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sin \left (2 t \right ) \left (17 c_{2} {\mathrm e}^{-t}+3\right )}{17}+{\mathrm e}^{-t} \cos \left (2 t \right ) c_{1} -\frac {12 \cos \left (2 t \right )}{17} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 45
DSolve[y''[t]+2*y'[t]+5*y[t]==3*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{17} e^{-t} \left (\left (-12 e^t+17 c_2\right ) \cos (2 t)+\left (3 e^t+17 c_1\right ) \sin (2 t)\right ) \]