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relations between derivatives
If y=sin(pi(x+1)^1/2) show that:
4(x+1)y''+2y'+(pi^2)y = 0
Now differentiate n times and find a relation between any 3 successive derivatives of y.
i can do the show that part, but how do i diff n times and find the relation?
4(x+1)y''+2y'+(pi^2)y = 0
Now differentiate n times and find a relation between any 3 successive derivatives of y.
i can do the show that part, but how do i diff n times and find the relation?
4(x + 1)y''' + 4y'' + 2y'' + (pi^2)y' = 0
4(x + 1)y''' + 6y'' + (pi^2)y' = 0
4(x + 1)y'''' + 4y''' + 6y''' + (pi^2)y'' = 0
4(x + 1)y'''' + 10y''' + (pi^2)y'' = 0
etc
4(x + 1)y^{(n + 2)} + (4n + 2)y^{(n + 1)} + (pi^2)y^{(n)} = 0
You might want to prove this result by induction.
[y^{(n)} is a "y" with a superscript "(n)". It is the nth derivative of y.]
4(x + 1)y''' + 6y'' + (pi^2)y' = 0
4(x + 1)y'''' + 4y''' + 6y''' + (pi^2)y'' = 0
4(x + 1)y'''' + 10y''' + (pi^2)y'' = 0
etc
4(x + 1)y^{(n + 2)} + (4n + 2)y^{(n + 1)} + (pi^2)y^{(n)} = 0
You might want to prove this result by induction.
[y^{(n)} is a "y" with a superscript "(n)". It is the nth derivative of y.]
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