Internal problem ID [15514]
Internal file name [OUTPUT/15515_Friday_May_10_2024_05_47_32_PM_11055370/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: 784.
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: 40
dsolve([diff(x(t),t$2)+diff(y(t),t)+x(t)=0,diff(x(t),t)+diff(y(t),t$2)=0],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} -\frac {1}{2} t^{2} c_{1} -c_{2} t -c_{3} \\ y \left (t \right ) &= \frac {1}{6} t^{3} c_{1} +\frac {1}{2} c_{2} t^{2}+c_{3} t +c_{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 61
DSolve[{x''[t]+y'[t]+x[t]==0,x'[t]+y''[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {c_1 t^2}{2}-\frac {c_4 t^2}{2}+c_2 t+c_1 \\ y(t)\to \frac {1}{6} (c_1+c_4) t^3-\frac {c_2 t^2}{2}+c_4 t+c_3 \\ \end{align*}