72.11.14 problem 26

Internal problem ID [14847]
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 3.4 page 310
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 07:17:36 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+10 y\\ y^{\prime }&=-x \left (t \right )+3 y \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 37

dsolve([diff(x(t),t)=-3*x(t)+10*y(t),diff(y(t),t)=-x(t)+3*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ y &= \frac {\cos \left (t \right ) c_{1}}{10}-\frac {c_{2} \sin \left (t \right )}{10}+\frac {3 c_{1} \sin \left (t \right )}{10}+\frac {3 c_{2} \cos \left (t \right )}{10} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 42

DSolve[{D[x[t],t]==-3*x[t]+10*y[t],D[y[t],t]==-x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 10 c_2 \sin (t)+c_1 (\cos (t)-3 \sin (t)) \\ y(t)\to c_2 (3 \sin (t)+\cos (t))-c_1 \sin (t) \\ \end{align*}