Internal problem ID [4647]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+5 y-6 \sin \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+5*y(t)=6*sin(t),y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-2 t} \sin \relax (t ) c_{2}+{\mathrm e}^{-2 t} \cos \relax (t ) c_{1}-\frac {3 \cos \relax (t )}{4}+\frac {3 \sin \relax (t )}{4} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 34
DSolve[y''[t]+4*y'[t]+5*y[t]==6*Sin[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {3}{4} (\cos (t)-\sin (t))+e^{-2 t} (c_2 \cos (t)+c_1 \sin (t)) \\ \end{align*}