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I have a few questions on the solutions:
The final questions for #3 aren't included: If one of the two homogeneous solutions blows up, is it mathematically possible for
a linear combination to remain bounded? Is it practically possible if the equation
represents a real system for the solution to remain bounded?
For #5, I am confused on how -cost*integral(tant) just becomes ln(cost).

Thank you!!

ldillon1 wrote:I have a few questions on the solutions:
The final questions for #3 aren't included: If one of the two homogeneous solutions blows up, is it mathematically possible for
a linear combination to remain bounded? Is it practically possible if the equation
represents a real system for the solution to remain bounded?
For #5, I am confused on how -cost*integral(tant) just becomes ln(cost).

Thank you!!

Yes it is possible for a linear combination to not blow up if the coefficient of the blowing up term is zero. In a real physical system, that is very unlikely that the initial conditions combine such that one of the coefficients in the solution is exactly zero.

I think the log cos is a typo. It seems to have dropped the cos(t) and the minus sign.