Internal problem ID [10189]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1866.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 y \left (t \right )+3 t\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+4 \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve({diff(x(t),t)+2*y(t)=3*t,diff(y(t),t)-2*x(t)=4},singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (2 t \right )+c_{1} \cos \left (2 t \right )-\frac {5}{4} \\ y \left (t \right ) &= -c_{2} \cos \left (2 t \right )+c_{1} \sin \left (2 t \right )+\frac {3 t}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.205 (sec). Leaf size: 47
DSolve[{x'[t]+2*y[t]==3*t,y'[t]-2*x[t]==4},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (2 t)-c_2 \sin (2 t)-\frac {5}{4} \\ y(t)\to \frac {3 t}{2}+c_2 \cos (2 t)+c_1 \sin (2 t) \\ \end{align*}