GATE EE 2016 Set 2 — Question 40
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Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs
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Question
Let be the solution of the differential equation with initial conditions and . Then the value of is _________.
Correct answer
7 to 7.5
Solution
The given differential equation is a second-order linear homogeneous equation with constant coefficients:The characteristic equation is:The roots are (repeated real roots). The general solution is:Applying the initial condition :Thus, . Now, find the derivative:Applying the second initial condition :The specific solution is . To find the value of :The value of is approximately 7.389, which falls within the range [7.0, 7.5].
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