72.10.6 problem 6

Internal problem ID [14817]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.2. page 277
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 07:17:09 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+4 y\\ y^{\prime }&=9 x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 34

dsolve([diff(x(t),t)=5*x(t)+4*y(t),diff(y(t),t)=9*x(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{9 t}-\frac {4 c_{2} {\mathrm e}^{-4 t}}{9} \\ y &= c_{1} {\mathrm e}^{9 t}+c_{2} {\mathrm e}^{-4 t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 74

DSolve[{D[x[t],t]==5*x[t]+4*y[t],D[y[t],t]==9*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{13} e^{-4 t} \left (c_1 \left (9 e^{13 t}+4\right )+4 c_2 \left (e^{13 t}-1\right )\right ) \\ y(t)\to \frac {1}{13} e^{-4 t} \left (9 c_1 \left (e^{13 t}-1\right )+c_2 \left (4 e^{13 t}+9\right )\right ) \\ \end{align*}