GATE CE 2021 Set 1 — Question 36
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Engineering Mathematics → Ordinary Differential Equations → Boundary Value Problems
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Question
The solution of the second-order differential equation with boundary conditions and is
Correct answer
(A) e^(-x) + (3e - 1)xe^(-x)
Solution
The given differential equation is .Step 1: Find the characteristic equation.
(repeated real roots)Step 2: Write the general solution.
Step 3: Apply boundary conditions to find constants and .
Condition 1:
Condition 2:
Step 4: Substitute constants back into the general solution.
This matches option (A).
(repeated real roots)Step 2: Write the general solution.
Step 3: Apply boundary conditions to find constants and .
Condition 1:
Condition 2:
Step 4: Substitute constants back into the general solution.
This matches option (A).
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