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23 = sint is a solution of the differential equation " + x = 0. nd at least one more solution of this equation.

23 = sint is a solution of the differential equation " + x = 0. nd at least one more solution of this equation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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21-e, 2 x3 = e. equation x" + x = 0. 5. Verify that x = sint is a solution of the differential By guessing, find at least one more solution of this equation.
Transcribed Image Text:21-e, 2 x3 = e. equation x" + x = 0. 5. Verify that x = sint is a solution of the differential By guessing, find at least one more solution of this equation.
Expert Solution
Verification

given that the differential equation is

x"+x=0           --------(1)

We need to calculate  the derivative of  x=sint and plug into the equation (1) to see whether it satisfy that or not.

If it satisfy the equation (1) we argue that it is the solution of the ode.

Now calculate the derivatives-

x'=cost

x"= - sint.

Now plug the values in the equation (1).

LHS -

x"+x = (-sint)+ (sint) =0

RHS=0

since LHS=RHS ,

So x=sint  is an solution  of the given  differential equation. 

(Proved)

 

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