Internal problem ID [14541]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-9 y=54 \sin \left (2 t \right ) t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)-9*y(t)=54*t*sin(2*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-3 t}+c_{1} {\mathrm e}^{3 t}-\frac {216 \cos \left (2 t \right )}{169}-\frac {54 t \sin \left (2 t \right )}{13} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 40
DSolve[y''[t]-9*y[t]==54*t*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_1 e^{3 t}+c_2 e^{-3 t}-\frac {54}{169} (13 t \sin (2 t)+4 \cos (2 t)) \]