78.28.3 problem 1 (c)

Internal problem ID [18473]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 10. Systems of First Order Equations. Section 56. Homogeneous Linear Systems with Constant Coefficients. Problems at page 505
Problem number : 1 (c)
Date solved : Tuesday, January 28, 2025 at 11:50:34 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 34

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

\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \\ y &= -\frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 46

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

\begin{align*} x(t)\to e^{3 t} (2 c_1 t+4 c_2 t+c_1) \\ y(t)\to e^{3 t} (c_2-(c_1+2 c_2) t) \\ \end{align*}