Internal problem ID [15515]
Internal file name [OUTPUT/15516_Friday_May_10_2024_05_47_32_PM_49721640/index.tex]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 20. The method of elimination.
Exercises page 212
Problem number: 785.
ODE order: 2.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown" Unable to solve or complete the solution.
Unable to parse ODE.
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve([diff(x(t),t$2)=3*x(t)+y(t),diff(y(t),t)=-2*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}-\frac {c_{2} {\mathrm e}^{t}}{2}-\frac {c_{3} {\mathrm e}^{t} t}{2}-\frac {c_{3} {\mathrm e}^{t}}{2} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{t}+c_{3} {\mathrm e}^{t} t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 125
DSolve[{x''[t]==3*x[t]+y[t],y'[t]==-2*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{9} e^{-2 t} \left (c_1 \left (e^{3 t} (3 t+5)+4\right )+c_2 \left (e^{3 t} (3 t+2)-2\right )+c_3 \left (e^{3 t} (3 t-1)+1\right )\right ) \\ y(t)\to \frac {1}{9} e^{-2 t} \left (c_1 \left (4-2 e^{3 t} (3 t+2)\right )+c_2 \left (e^{3 t} (2-6 t)-2\right )+c_3 \left (e^{3 t} (8-6 t)+1\right )\right ) \\ \end{align*}