Internal problem ID [12385]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 8.3 Systems of Linear Differential Equations (Variation of Parameters).
Problems page 514
Problem number: Problem 5(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-2 y+24 \sin \left (t \right )\\ y^{\prime }&=9 x \left (t \right )-3 y+12 \cos \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 44
dsolve([diff(x(t),t) = 3*x(t)-2*y(t)+24*sin(t), diff(y(t),t) = 9*x(t)-3*y(t)+12*cos(t), x(0) = 1, y(0) = -1], singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {4 \sin \left (3 t \right )}{3}+\cos \left (3 t \right )+9 \sin \left (t \right ) \\ y \left (t \right ) &= \frac {7 \cos \left (3 t \right )}{2}-\frac {\sin \left (3 t \right )}{2}-\frac {9 \cos \left (t \right )}{2}+\frac {51 \sin \left (t \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 50
DSolve[{x'[t]==3*x[t]-2*y[t]+24*Sin[t],y'[t]==9*x[t]-3*y[t]+12*Cos[t]},{x[0]==1,y[0]==-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 9 \sin (t)-\frac {4}{3} \sin (3 t)+\cos (3 t) \\ y(t)\to \frac {1}{2} (51 \sin (t)-\sin (3 t)-9 \cos (t)+7 \cos (3 t)) \\ \end{align*}