GATE EC 2014 Set 4 — Question 36
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Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs
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Question
With initial values , the solution of the differential equation at is _____.
Correct answer
0.53 to 0.55
Solution
The given differential equation is a second-order linear homogeneous equation with constant coefficients:The characteristic equation is:The roots are real and repeated: .
The general solution is:Using the initial condition :Differentiating to find :Using the initial condition :Since , .
The particular solution is:At :Using :The value is approximately 0.54.
The general solution is:Using the initial condition :Differentiating to find :Using the initial condition :Since , .
The particular solution is:At :Using :The value is approximately 0.54.
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