GATE EE 2016 Set 2 — Question 18
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Engineering Mathematics → Differential Equations → Higher-Order Linear ODEs
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Question
The solution of the differential equation, for , with initial conditions and , is ( denotes the unit step function),
Correct answer
(A) t e^(-t) u(t)
Solution
The given differential equation is a second-order linear homogeneous equation with constant coefficients: . The characteristic equation is , which has a repeated root . The general solution is . Applying the initial conditions:
1..
2.Then . Its derivative is .
3.Applying the second initial condition: .
Thus, . Since the solution is for , we multiply by the unit step function , giving .Continue learning with Success Tracker
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