Internal problem ID [9445]
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 }\relax (t )&=-2 y \relax (t )+3 t\\ y^{\prime }\relax (t )&=2 x \relax (t )+4 \end {align*}
✓ Solution by Maple
Time used: 0.066 (sec). Leaf size: 39
dsolve({diff(x(t),t)+2*y(t)=3*t,diff(y(t),t)-2*x(t)=4},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \sin \left (2 t \right ) c_{2}+\cos \left (2 t \right ) c_{1}-\frac {5}{4} \] \[ y \relax (t ) = -\cos \left (2 t \right ) c_{2}+\sin \left (2 t \right ) c_{1}+\frac {3 t}{2} \]
✓ Solution by Mathematica
Time used: 0.042 (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*}