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Homework Statement
Determine all the solutions, if any, to the given boundary value problem by first finding a general solution to the differential equation:
y" + y = 0 ; 0<x<2π
y(0)=0 , y(2π)=1
The attempt at a solution
So the general solution is given by: y = c1sin(x) + c2cos(x)
Substituting in the boundary conditions we get:
y(0)=0=c2 ==> c2=0
y(2π)=1=c2 ==> c2=1
Since the above is contradictory, does it mean that there are no solutions to this boundary value problem?
Determine all the solutions, if any, to the given boundary value problem by first finding a general solution to the differential equation:
y" + y = 0 ; 0<x<2π
y(0)=0 , y(2π)=1
The attempt at a solution
So the general solution is given by: y = c1sin(x) + c2cos(x)
Substituting in the boundary conditions we get:
y(0)=0=c2 ==> c2=0
y(2π)=1=c2 ==> c2=1
Since the above is contradictory, does it mean that there are no solutions to this boundary value problem?