Question

Differential equation problem.

Answer 1

Just wondering I have to derive this equation twice and sub back in?

Answer 2

i see product rule, chain rule, and power rule at first glance

Answer 3

To show that \[x(t)=t^{-3}\cos(4 \ln t)\]
is a solution, you will have to plug it into your equation, such that:
\[t^2\frac{d^2}{dt^2}(t^{-3}\cos(4 \ln t))+7\tfrac{d}{dt}((t^{-3}\cos(4 \ln t))+25((t^{-3}\cos(4 \ln t))=0\]

and do the algebra/calculus to show that the left side simplifies to 0

Answer 4

Me too, I did it out and factorised out to be -t^-4((3(cos4lnt))*4sin(4lnt))

Answer 5

Sorry for the mess, I need to learn latex.