Internal problem ID [13148]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\pi ^{2} x \left (t \right )+\frac {187 y}{5}\\ y^{\prime }&=\sqrt {555}\, x \left (t \right )+\frac {400617 y}{5000} \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve([diff(x(t),t) = Pi^2*x(t)+187/5*y(t), diff(y(t),t) = 555^(1/2)*x(t)+400617/5000*y(t), x(0) = 0, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= 0 \\ y \left (t \right ) &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 10
DSolve[{x'[t]==Pi^2*x[t]+374/10*y[t],y'[t]==Sqrt[555]*x[t]+801234/10000*y[t]},{x[0]==0,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}