its asking me to find rewrite my answer of d^2y/dx^2 in terms of y. My answer was -
cos(x*k)*c1*k^2-sin(x*k)*c2*k^2 which was correct but im lost on putting it in terms of y. I've
tried multiplying both sides by dx^2 and integrating twice but im not getting the right answer.
Am i on the right track there? It then asks to find the general solution to d^y/dx^2=-25y which i
havent been able to do without the first part and am not sure if i would be doing that right either.
Solution
i did not understand your question properly.i think you want solution of d^y/dx^2=-
25y Assume a solution will be proportional to e^(lambda x) for some constant lambda.
Substitute y(x) = e^(lambda x) into the differential equation: ( d^2 )/( dx^2)(e^(lambda x))+25
e^(lambda x) = 0 Substitute ( d^2 )/( dx^2)(e^(lambda x)) = lambda^2 e^(lambda x): lambda^2
e^(lambda x)+25 e^(lambda x) = 0 Factor out e^(lambda x): (lambda^2+25) e^(lambda x) = 0
Since e^(lambda x) !=0 for any finite lambda, the zeros must come from the polynomial:
lambda^2+25 = 0 Solve for lambda: lambda = 5 i or lambda = -5 i The roots lambda =