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Yes but when you plug them into that determinant they are going to become 0.
There are infinitely many solutions.
What is the other solution?
There should be..because v1 and v2 are linearly independent
That is what I am saying. If there is only one solution. Is there another solution?
But then don't we find that v1(x)=v2(x) ? Or not? I haven't understood...
Of course you do, but you already got the solution to DE earlier.
Can't I just write that the Wronskian is equal to:
That is true but have you used the solutions to compute the wronskian?
Because the exercise says that v1,v2 are solutions of the differential equation so thatis not constant..So,
How do you know the two solutions are linearly independent?
Because there is a theorem that says that if two solutions of a differential equation are linearly independent,their Wronskian is nonzero!!!
I do not know why it should be non zero.
But the Wronkian should be nonzero..So,what do I have to do??