Internal problem ID [15535]
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: 812.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )+\tan \left (t \right )^{2}-1\\ y^{\prime }\left (t \right )&=\tan \left (t \right )-x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 30
dsolve([diff(x(t),t)=y(t)+tan(t)^2-1,diff(y(t),t)=tan(t)-x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+\tan \left (t \right ) \\ y \left (t \right ) &= c_{2} \cos \left (t \right )-c_{1} \sin \left (t \right )+2 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 34
DSolve[{x'[t]==y[t]+Tan[t]^2-1,y'[t]==Tan[t]-x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \tan (t)+c_1 \cos (t)+c_2 \sin (t) \\ y(t)\to c_2 \cos (t)-c_1 \sin (t)+2 \\ \end{align*}