GATE EC 2019 Set 1 — Question 53
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Engineering Mathematics → Differential Equations → Euler-Cauchy Equations
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Question
Consider the homogeneous ordinary differential equationwith as a general solution. Given thatthe value of , rounded off to two decimal places, is ________.
Correct answer
5.24 to 5.26
Solution
This is a Cauchy-Euler equation. Let , then and , where .
Substituting these into the differential equation:The characteristic equation is , which has roots .
The general solution is , or in terms of :Applying the boundary conditions:
1)
2)
Subtracting (1) from (2): .
Then .
The specific solution is .
Calculating :
Substituting these into the differential equation:The characteristic equation is , which has roots .
The general solution is , or in terms of :Applying the boundary conditions:
1)
2)
Subtracting (1) from (2): .
Then .
The specific solution is .
Calculating :
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