- #1

gikiian

- 98

- 0

Given that the solution is of the form [itex]sin(ωt+ø)[/itex], I plug this form into the original ODE and obtain [itex]ω=+\sqrt\frac{k}{m},-\sqrt\frac{k}{m}[/itex].

And hence, I obtain two solutions of the ODE as follows:

[itex]x_{1}(t)=Asin(\sqrt\frac{k}{m}t+ø), x_{2}(t)=Bsin(-\sqrt\frac{k}{m}t+ø)[/itex]

Next, I check for the linear independence of the two solutions using the 2x2 Wronskian matrix and obtain [itex]Wronskian=-2ωsin(ø)[/itex] which vanishes at ø=0 or ω=0, implying that the two solutions are not linearly independent.

How can I find the second solution of the second order ODE?