Internal problem ID [14036]
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 (j).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-y \left (t \right )\\ y^{\prime }\left (t \right )&=4 x \left (t \right )+24 t \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve([diff(x(t),t) = -y(t), diff(y(t),t) = 4*x(t)+24*t, x(0) = 0, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= 3 \sin \left (2 t \right )-6 t \\ y \left (t \right ) &= -6 \cos \left (2 t \right )+6 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 24
DSolve[{x'[t]==-y[t],y'[t]==4*x[t]+24*t},{x[0]==0,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 \sin (2 t)-6 t \\ y(t)\to 12 \sin ^2(t) \\ \end{align*}