Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\dfrac{d^2x(t)}{dt^2}+x(t)=0, \: t>0$ such that $x_1(0)=1, \dfrac{dx_1(t)}{dt} \bigg \vert_{t=0}=0$, $x_2(0)=0, \dfrac{dx_2(t)}{dt}\bigg \vert _{t=0}=1$. The Wronskian $W(t)=\begin{bmatrix} x_1(t) & x_2(t)\\ \\ \dfrac{dx_1(t)}{dt} & \dfrac{dx_2(t)}{dt} \end{bmatrix}$ at $t=\pi /2$ is $1$ $-1$ $0$ $\pi /2$

asked
Feb 19, 2017
in Differential Equations
Arjun
24.6k points