Internal problem ID [14575]
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: 70 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 y^{\prime \prime }+4 y^{\prime }+37 y=\cos \left (3 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = a, y^{\prime }\left (\pi \right ) = a] \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 55
dsolve([4*diff(y(t),t$2)+4*diff(y(t),t)+37*y(t)=cos(3*t),y(0) = a, D(y)(Pi) = a],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (-290 a -72\right ) \sin \left (3 t \right ) {\mathrm e}^{-\frac {t}{2}+\frac {\pi }{2}}}{870}+\left (\frac {\sin \left (3 t \right )}{6}+\cos \left (3 t \right )\right ) \left (a -\frac {1}{145}\right ) {\mathrm e}^{-\frac {t}{2}}+\frac {\cos \left (3 t \right )}{145}+\frac {12 \sin \left (3 t \right )}{145} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 75
DSolve[{4*y''[t]+4*y'[t]+37*y[t]==Cos[3*t],{y[0]==a,y'[Pi]==a}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{870} e^{-t/2} \left (6 \left (145 a+e^{t/2}-1\right ) \cos (3 t)-\left (145 \left (2 e^{\pi /2}-1\right ) a-72 e^{t/2}+72 e^{\pi /2}+1\right ) \sin (3 t)\right ) \]