Internal problem ID [14540]
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: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+13 y=25 \sin \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve(diff(y(t),t$2)-6*diff(y(t),t)+13*y(t)=25*sin(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (3 c_{2} {\mathrm e}^{3 t}+3\right ) \sin \left (2 t \right )}{3}+\cos \left (2 t \right ) {\mathrm e}^{3 t} c_{1} +\frac {4 \cos \left (2 t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 38
DSolve[y''[t]-6*y'[t]+13*y[t]==25*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (\frac {4}{3}+c_2 e^{3 t}\right ) \cos (2 t)+\left (1+c_1 e^{3 t}\right ) \sin (2 t) \]