Internal problem ID [15542]
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: 819.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-5 y \left (t \right )+4 t -1\\ y^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )+t \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 12
dsolve([diff(x(t),t) = 4*x(t)-5*y(t)+4*t-1, diff(y(t),t) = x(t)-2*y(t)+t, x(0) = 0, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= -t \\ y \left (t \right ) &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 12
DSolve[{x'[t]==4*x[t]-5*y[t]+4*t-1,y'[t]==x[t]-2*y[t]+t},{x[0]==0,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -t \\ y(t)\to 0 \\ \end{align*}