Internal problem ID [12550]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-4 x \left (t \right )-10 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 59
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 c_{2} \sin \left (3 t \right )+3 c_{1} \cos \left (3 t \right )+c_{2} \cos \left (3 t \right )\right )}{10} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 67
DSolve[{x'[t]==-4*x[t]-10*y[t],y'[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*}