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Engineering Maths · Q29

Differential Equations

Engineering and GATE · Engineering Maths · question 29

Q29

Consider two solutions x(t) = x1(t) and x(t) = x2(t) of the differential equation d^2 x ( t ) d t^2 + x ( t ) = 0,\, t > 0, such that x_2 = 0,\, . d x_2 ( t ) dt |_ t = 0 = 1. The Wronskian \[ W ( t ) = | array*20c x_1 ( t )& x_2 ( t ) \\ d x_1 ( t ) dt& d x_2 ( t ) dt array |\] at t = /2 is

Consider two solutions x(t) = x1(t) and x(t) = x2(t) of the differential equation     such that     The Wronskian {\text{W}}\left( {\text{t}} \right) = \left| {\begin{array}{*{20}{c}} {{{\text{x}}_1}\left( {\text{t}} \right)}&{{{\text{x}}_2}\left( {\text{t}} \right)} \\ {\frac{{{\text{d}}{{\text{x}}_1}\left( {\text{t}} \right)}}{{{\text{dt}}}}}&{\frac{{{\text{d}}{{\text{x}}_2}\left( {\text{t}} \right)}}{{{\text{dt}}}}} \end{array}} \right|     at  is
A.
1
Answer
B.
-1
C.
0
D.

Answer: Option A

Solution

Answer: Option A
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