Question: Question: Consider the oDE x'' +3x' + 2x=e st for some constant s. a) Find the homogeneous solution fo the ODE. b) Find a particular

Question: Consider the oDE x'' +3x' + 2x=e^st for some constant s.

a) Find the homogeneous solution fo the ODE.

b) Find a particular solution of the ODE of the form Ae^st, where s does not cause resonance.

c) Using your particular solution of the form Ae^st, find all values of s such that A is equal or bigger than 100.

Attempt: For part a), I found m= -1 and -2 by factoring out the given equation, and wrote my homogeneous equation as x= C₁e^-t +C₂e^-2t.

Then, for part b, I got A as 1/(s^2+3s+2) but not sure if this is correct! Am I supposed to find a numerical value for A?

For part c, I know that I'm supposed to make inequality equation between the A value I found and 100, then sovle for S value. But should the answer be in an interval form?

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