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ODE: 4. Consider u" + u = 0 , with boundary conditions u(0)= u(L)=0 where L...

ODE: 4. Consider u" + u = 0 , with boundary conditions u(0)= u(L)=0 where L is fixed positive constant. So, u=0 is a sol.

a. Is this sol unique and

b. to what extend does uniqueness depend on the value of L.

Give convincing reasons or proof for your answers.

SUBJECT: ORDINARY DIFFERENTIAL EQUATION AND PARTIAL DIFFERENTIAL EQUATIONS

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Answer #1

I have solved the differential equation and observed that if

then the solution u=0 is not unique but if

then the solution u=0 is unique.

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