Internal problem ID [5155]
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]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=6 \sin \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = {\mathrm e}^{-2 t} \sin \left (t \right ) c_{2} +{\mathrm e}^{-2 t} \cos \left (t \right ) c_{1} -\frac {3 \cos \left (t \right )}{4}+\frac {3 \sin \left (t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 36
DSolve[y''[t]+4*y'[t]+5*y[t]==6*Sin[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (-\frac {3}{4}+c_2 e^{-2 t}\right ) \cos (t)+\left (\frac {3}{4}+c_1 e^{-2 t}\right ) \sin (t) \]