GATE CE 2019 Set 1 — Question 54
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Engineering Mathematics → Ordinary Differential Equations → Euler-Cauchy Equations
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Question
Consider the ordinary differential equation . Given the values of and , the value of (round off to 1 decimal place), is ________
Correct answer
5.9 to 6.1
Solution
The given equation is a Cauchy-Euler differential equation: .
Assume a solution of the form . The auxiliary equation is:
The general solution is .
Using boundary conditions:
1)
2)
Subtracting the first from the second: .
Then .
The specific solution is .
For : .
Assume a solution of the form . The auxiliary equation is:
The general solution is .
Using boundary conditions:
1)
2)
Subtracting the first from the second: .
Then .
The specific solution is .
For : .
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