GATE EE 2015 Set 1 — Question 37
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Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs
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Question
A solution of the ordinary differential equation is such that and . The value of is ________.
Correct answer
-3 to -3
Solution
The characteristic equation for the differential equation is .
Solving for :
.
The general solution is .
Using the initial condition :
.
Using the condition :
.
Equating the two expressions for :
.
Then .
The solution is .
The derivative is .
At , .
Solving for :
.
The general solution is .
Using the initial condition :
.
Using the condition :
.
Equating the two expressions for :
.
Then .
The solution is .
The derivative is .
At , .
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