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GATE ME 2014 Set 3 — Question 37

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MCQ+2 / -0.67MediumHigher-Order Linear ODEsDifferential EquationsEngineering Mathematics

Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs

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Question

Consider two solutions x(t)=x1(t)x(t) = x_1(t) and x(t)=x2(t)x(t) = x_2(t) of the differential equation d2x(t)dt2+x(t)=0,t>0\frac{d^2x(t)}{dt^2} + x(t) = 0, t > 0, such that x1(0)=1,dx1(t)dt∣t=0=0,x2(0)=0,dx2(t)dt∣t=0=1x_1(0) = 1, \left. \frac{dx_1(t)}{dt} \right|_{t=0} = 0, x_2(0) = 0, \left. \frac{dx_2(t)}{dt} \right|_{t=0} = 1. The Wronskian W(t)=∣x1(t)x2(t)dx1(t)dtdx2(t)dt∣W(t) = \begin{vmatrix} x_1(t) & x_2(t) \\ \frac{dx_1(t)}{dt} & \frac{dx_2(t)}{dt} \end{vmatrix} at t=π/2t = \pi/2 is
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