69.1.133 problem 192

Internal problem ID [14286]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 192
Date solved : Tuesday, January 28, 2025 at 06:25:45 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-4 x \left (t \right )-10 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-2 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 58

dsolve([diff(x(t),t)=-4*x(t)-10*y(t),diff(y(t),t)=x(t)-2*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 67

DSolve[{D[x[t],t]==-4*x[t]-10*y[t],D[y[t],t]==x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{3} e^{-3 t} (3 c_1 \cos (3 t)-(c_1+10 c_2) \sin (3 t)) \\ y(t)\to \frac {1}{3} e^{-3 t} (3 c_2 \cos (3 t)+(c_1+c_2) \sin (3 t)) \\ \end{align*}