Internal problem ID [15537]
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. Methods of integrating
nonhomogeneous linear systems with constant coefficients. Exercises page 234
Problem number: 814.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+\frac {1}{\cos \left (t \right )} \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 48
dsolve([diff(x(t),t)=y(t),diff(y(t),t)=-x(t)+1/cos(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+\sin \left (t \right ) t +\cos \left (t \right ) \ln \left (\cos \left (t \right )\right ) \\ y \left (t \right ) &= c_{2} \cos \left (t \right )-c_{1} \sin \left (t \right )+\cos \left (t \right ) t -\sin \left (t \right ) \ln \left (\cos \left (t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 43
DSolve[{x'[t]==y[t],y'[t]==-x[t]+1/Cos[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to (t+c_2) \sin (t)+\cos (t) (\log (\cos (t))+c_1) \\ y(t)\to (t+c_2) \cos (t)-\sin (t) (\log (\cos (t))+c_1) \\ \end{align*}