15.17.6 problem 6

Internal problem ID [3242]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 26, page 115
Problem number : 6
Date solved : Monday, January 27, 2025 at 07:27:20 AM
CAS classification : system_of_ODEs

\begin{align*} 5 \frac {d}{d t}y \left (t \right )-3 \frac {d}{d t}x \left (t \right )-5 y \left (t \right )&=5 t\\ 3 \frac {d}{d t}x \left (t \right )-5 \frac {d}{d t}y \left (t \right )-2 x \left (t \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 27

dsolve([5*diff(y(t),t)-3*diff(x(t),t)-5*y(t)=5*t,3*diff(x(t),t)-5*diff(y(t),t)-2*x(t)=0],singsol=all)
 

\begin{align*} x \left (t \right ) &= \frac {5}{2}+{\mathrm e}^{\frac {2 t}{5}} c_{1} \\ y \left (t \right ) &= -1-\frac {2 \,{\mathrm e}^{\frac {2 t}{5}} c_{1}}{5}-t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 43

DSolve[{5*D[y[t],t]-3*D[x[t],t]-5*y[t]==5*t,3*D[x[t],t]-5*D[y[t],t]-2*x[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {5}{6} \left (3+2 c_1 e^{2 t/5}\right ) \\ y(t)\to -t-\frac {2}{3} c_1 e^{2 t/5}-1 \\ \end{align*}