GATE CE 2018 Set 1 — Question 48
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Engineering Mathematics → Ordinary Differential Equations → Higher-Order Linear ODEs
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Question
The solution (up to three decimal places) at of the differential equation subject to boundary conditions and is ______
Correct answer
0.36 to 0.37
Solution
The given differential equation is a second-order linear homogeneous equation with constant coefficients: .
The characteristic equation is , which factors as . The roots are (repeated).
The general solution is .Applying the boundary conditions:
1) .
2) .
.So, the specific solution is .
At , .
Rounding to three decimal places, we get 0.368.
The characteristic equation is , which factors as . The roots are (repeated).
The general solution is .Applying the boundary conditions:
1) .
2) .
.So, the specific solution is .
At , .
Rounding to three decimal places, we get 0.368.
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