Internal problem ID [13717]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 38. Systems of differential equations. A starting point. Additional Exercises.
page 786
Problem number: 38.10 (k).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-13 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+152 \cos \left (t \right )^{4}-152 \cos \left (t \right )^{2}+19-104 \sin \left (t \right ) \cos \left (t \right )^{3}+52 \sin \left (t \right ) \cos \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 13, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 27
dsolve([diff(x(t),t) = 4*x(t)-13*y(t), diff(y(t),t) = x(t)+19*cos(4*t)-13*sin(4*t), x(0) = 13, y(0) = 0],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = 13 \cos \left (4 t \right )+13 \sin \left (4 t \right ) y \left (t \right ) = 8 \sin \left (4 t \right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 25
DSolve[{x'[t]==4*x[t]-13*y[t],y'[t]==x[t]+19*Cos[4*t]-13*Sin[4*t]},{x[0]==13,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 13 (\sin (4 t)+\cos (4 t)) y(t)\to 8 \sin (4 t) \end{align*}