Internal problem ID [12549]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 191.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=5 x \left (t \right )+6 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 78
dsolve([diff(x(t),t)=2*x(t)-3*y(t),diff(y(t),t)=5*x(t)+6*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{4 t} \left (\sin \left (\sqrt {11}\, t \right ) c_{1} +\cos \left (\sqrt {11}\, t \right ) c_{2} \right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{4 t} \left (\sin \left (\sqrt {11}\, t \right ) \sqrt {11}\, c_{2} -\cos \left (\sqrt {11}\, t \right ) \sqrt {11}\, c_{1} -2 \sin \left (\sqrt {11}\, t \right ) c_{1} -2 \cos \left (\sqrt {11}\, t \right ) c_{2} \right )}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 99
DSolve[{x'[t]==2*x[t]-3*y[t],y'[t]==5*x[t]+6*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{4 t} \cos \left (\sqrt {11} t\right )-\frac {(2 c_1+3 c_2) e^{4 t} \sin \left (\sqrt {11} t\right )}{\sqrt {11}} \\ y(t)\to c_2 e^{4 t} \cos \left (\sqrt {11} t\right )+\frac {(5 c_1+2 c_2) e^{4 t} \sin \left (\sqrt {11} t\right )}{\sqrt {11}} \\ \end{align*}