Internal problem ID [10181]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1858.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=a y \left (t \right )\\ y^{\prime }\left (t \right )&=b x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 64
dsolve({diff(x(t),t)=a*y(t),diff(y(t),t)=b*x(t)},singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\sqrt {a}\, \sqrt {b}\, t}+c_{2} {\mathrm e}^{-\sqrt {a}\, \sqrt {b}\, t} \\ y \left (t \right ) &= \frac {\sqrt {b}\, \left (c_{1} {\mathrm e}^{\sqrt {a}\, \sqrt {b}\, t}-c_{2} {\mathrm e}^{-\sqrt {a}\, \sqrt {b}\, t}\right )}{\sqrt {a}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 158
DSolve[{x'[t]==a*y[t],y'[t]==b*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {e^{-\sqrt {a} \sqrt {b} t} \left (\sqrt {b} c_1 \left (e^{2 \sqrt {a} \sqrt {b} t}+1\right )+\sqrt {a} c_2 \left (e^{2 \sqrt {a} \sqrt {b} t}-1\right )\right )}{2 \sqrt {b}} \\ y(t)\to \frac {e^{-\sqrt {a} \sqrt {b} t} \left (\sqrt {b} c_1 \left (e^{2 \sqrt {a} \sqrt {b} t}-1\right )+\sqrt {a} c_2 \left (e^{2 \sqrt {a} \sqrt {b} t}+1\right )\right )}{2 \sqrt {a}} \\ \end{align*}