72.15.3 problem 7

Internal problem ID [14884]
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
Date solved : Tuesday, January 28, 2025 at 07:18:06 AM
CAS classification : system_of_ODEs

\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

\begin{align*} x \left (0\right ) = 0\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 9

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 &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 10

DSolve[{D[x[t],t]==Pi^2*x[t]+374/10*y[t],D[y[t],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*}