Internal problem ID [15544]
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: 821.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=t^{2}-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+t \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve([diff(x(t),t)+y(t)=t^2,diff(y(t),t)-x(t)=t],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+t \\ y \left (t \right ) &= t^{2}-c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right )-1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 36
DSolve[{x'[t]+y[t]==t^2,y'[t]-x[t]==t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t+c_1 \cos (t)-c_2 \sin (t) \\ y(t)\to t^2+c_2 \cos (t)+c_1 \sin (t)-1 \\ \end{align*}