Differential equation (will rate life saver, but iff explanation is given)

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The equation I have is a homogeneous equation, assume k issmall:

I was using variation of parameters to solve this. By doing this Iget:

The book gives an answer of a similar thing:

Is it legitimate if I expand the answer I got using Euler'sequations (i.e. exp(ix)=cosx+ i sinx)

to get and just call the the A+B in front of cosand the i(A-B) in front of the sin just some arbitrary constant sayC and D respectively to get the form the book gives me? Please alsocorrect me if my method of solving the diff eq is incorrect. The iin front of the (A-B) worries me, but I figured a constant is aconstant, real or imaginary and it would just be absorbed into anew constant D.

Answers (1)

  • Anonymous
    Rating:5 stars

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