Internal problem ID [15538]
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 23.2 The method of undetermined
coefficients. Exercises page 239
Problem number: 815.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )\\ y^{\prime }\left (t \right )&=1-x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve([diff(x(t),t)=y(t),diff(y(t),t)=1-x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+1 \\ y \left (t \right ) &= c_{2} \cos \left (t \right )-c_{1} \sin \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 32
DSolve[{x'[t]==y[t],y'[t]==1-x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (t)+c_2 \sin (t)+1 \\ y(t)\to c_2 \cos (t)-c_1 \sin (t) \\ \end{align*}