72.10.7 problem 7

Internal problem ID [14818]
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 : 7
Date solved : Tuesday, January 28, 2025 at 07:17:09 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+4 y\\ y^{\prime }&=x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 35

dsolve([diff(x(t),t)=3*x(t)+4*y(t),diff(y(t),t)=1*x(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 71

DSolve[{D[x[t],t]==3*x[t]+4*y[t],D[y[t],t]==1*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{5} e^{-t} \left (c_1 \left (4 e^{5 t}+1\right )+4 c_2 \left (e^{5 t}-1\right )\right ) \\ y(t)\to \frac {1}{5} e^{-t} \left (c_1 \left (e^{5 t}-1\right )+c_2 \left (e^{5 t}+4\right )\right ) \\ \end{align*}