We have this system of equations:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\begin{cases}

x'= -x + 2y & (1)\\

y' = -2x - y + e^{-t} & (2)

\end{cases}

[/tex]

where [itex]x(0) = 0 ; y(0) = 0[/itex]

We apply the Laplace transform on (1) and (2) and get:

[tex]

(s + 1)X - 2Y = 0\\

2X + (s + 1)Y = \frac{1}{s + 1}

[/tex]

We can use elimination here, but can we apply Cramer's Rule? We find the determinant [itex]D = (s + 1)^2 + 4[/itex], and to find [itex]X_s[/itex] and [itex]Y_s[/itex], we use a certain formula. Is this applicabale here?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Cramer's Rule application in differential equations

Loading...

Similar Threads for Cramer's Rule application | Date |
---|---|

I Chain rule found in MIT video | Jul 14, 2016 |

Chain rule | Jan 23, 2016 |

Differential equations and Cramer's rule | Apr 16, 2014 |

Cramer's Rule | Dec 3, 2006 |

**Physics Forums - The Fusion of Science and Community**