72.10.4 problem 4

Internal problem ID [14815]
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 : 4
Date solved : Tuesday, January 28, 2025 at 07:17:07 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 28

dsolve([diff(x(t),t)=2*x(t)+1*y(t),diff(y(t),t)=-x(t)+4*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 44

DSolve[{D[x[t],t]==2*x[t]+1*y[t],D[y[t],t]==-x[t]+4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

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