Internal problem ID [15539]
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: 816.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )-2 t \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 37
dsolve([diff(x(t),t)=3-2*y(t),diff(y(t),t)=2*x(t)-2*t],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (2 t \right )+c_{1} \cos \left (2 t \right )+t \\ y \left (t \right ) &= -c_{2} \cos \left (2 t \right )+c_{1} \sin \left (2 t \right )+1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 41
DSolve[{x'[t]==3-2*y[t],y'[t]==2*x[t]-2*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t+c_1 \cos (2 t)-c_2 \sin (2 t) \\ y(t)\to c_2 \cos (2 t)+c_1 \sin (2 t)+1 \\ \end{align*}