Consider two solutions x(t) = x1(t) and x(t) = x2(t) of the differential equation \(\frac{{{d^2}x\left( t \right)}}{{d{t^2}}} + x\left( t \right) = 0,\;t > 0\), such that\(\ x_{1}(0)=1,\ {\left. {\frac{{d{x_1}\left( t \right)}}{{dt}}} \right|_{t = 0}} = 0,\;{x_2}\left( 0 \right) = 0,{\left. {\frac{{d{x_2}\left( t \right)}}{{dt}}} \right|_{t = 0}} = 1\)The Wronskian \(W\left( t \right) = \left| {\begin{array}{*{20}{c}} {{x_1}\left( t \right)}&{{x_2}\left( t \right)}\\ {\frac{{d{x_1}\left( t \right)}}{{dt}}}&{\frac{{d{x_2}\left( t \right)}}{{dt}}} \end{array}} \right|\) at \(t = \frac{\pi}{2}\) is

Consider two solutions x(t) = x1(t) and x(t) = x2(t) of the differenti

1.	Consider two solutions x(t) = x1(t) and x(t) = x2(t) of the differential equation \(\frac{{{d^2}x\left( t \right)}}{{d{t^2}}} + x\left( t \right) = 0,\;t > 0\), such that\(\ x_{1}(0)=1,\ {\left. {\frac{{d{x_1}\left( t \right)}}{{dt}}} \right\|_{t = 0}} = 0,\;{x_2}\left( 0 \right) = 0,{\left. {\frac{{d{x_2}\left( t \right)}}{{dt}}} \right\|_{t = 0}} = 1\)The Wronskian \(W\left( t \right) = \left\| {\begin{array}{*{20}{c}} {{x_1}\left( t \right)}&{{x_2}\left( t \right)}\\ {\frac{{d{x_1}\left( t \right)}}{{dt}}}&{\frac{{d{x_2}\left( t \right)}}{{dt}}} \end{array}} \right\|\) at \(t = \frac{\pi}{2}\) is
A.	1
B.	-1
C.	0
D.	π/2
Answer» B. -1

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