GATE ME 2023 Set 1 — Question 49
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Engineering Mathematics → Differential Equations → Euler-Cauchy Equation
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Question
Consider the second-order linear ordinary differential equationwith the initial conditionsThe value of at equals _________.
Correct answer
8.999 to 9.001
Solution
The given equation is a Cauchy-Euler equation of the form .
Substituting , we get the characteristic equation:
The general solution is .
Using the initial conditions:
1)
2)
Solving the system of equations:
Thus, the specific solution is .
At :
.
Substituting , we get the characteristic equation:
The general solution is .
Using the initial conditions:
1)
2)
Solving the system of equations:
Thus, the specific solution is .
At :
.
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