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This is not a homework problem, I just want to understand some theory behind this mathematical method.
Specifically, if we know that one solution is y_{1}(t), then why is the second solution in the form
Where v(t) is the function that you need to solve for. Why does this assumption always work?
Specifically, if we know that one solution is y_{1}(t), then why is the second solution in the form
y_{2}(t) = v(t) * y_{1}(t)?
Where v(t) is the function that you need to solve for. Why does this assumption always work?