diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md index b8601b08f1071c3ee419c7e5d44bcfa59031d37c..52868478bce35d7a2b774e70faf05cf42f9ea1e9 100644 --- a/src/8_differential_equations_2.md +++ b/src/8_differential_equations_2.md @@ -153,29 +153,6 @@ $$f(x) = e^{\lambda_1 x}, \ x e^{\lambda_1 x} , \ \cdots, \ x^{m_{1}-1} e^{\lamb $$y'' + Ey = 0.$$ - Let us reduce this second order equation to a system of two first order - equations. Define - - $$y_1=y$$ - $$y_2=y'.$$ - - Writing $**y**= \begin{bmatrix} - y_1 \\ - y_2 \\ - \end{bmatrix}$, the DE can be written, - - $$\dot{**y**} = \begin{bmatrix} - y_2 \\ - -E y_1 \\ - \end{bmatrix}$$ - $$\dot{**y**} = \begin{bmatrix} - 0 & 1 \\ - -E & 0 \\ - \end{bmatrix} \begin{bmatrix} - y_1 \\ - y_2 \\ - \end{bmatrix}.$$ - The characteristic polynomial of this equation is $$P(\lambda) = \lambda^2 + E.$$