Internal problem ID [12551]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 193.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=12 x \left (t \right )+18 y \left (t \right )\\ y^{\prime }\left (t \right )&=-8 x \left (t \right )-12 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve([diff(x(t),t)=12*x(t)+18*y(t),diff(y(t),t)=-8*x(t)-12*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} t +c_{2} \\ y \left (t \right ) &= \frac {1}{18} c_{1} -\frac {2}{3} c_{1} t -\frac {2}{3} c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[{x'[t]==12*x[t]+18*y[t],y'[t]==-8*x[t]-12*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 12 c_1 t+18 c_2 t+c_1 \\ y(t)\to c_2-4 (2 c_1+3 c_2) t \\ \end{align*}