Question

(D^3-5D+6)y = e^2x + e^3x​

Answer 1

Answer:

solve:

The solution to the homogeneous part of the equation is

explore:

yh = C1e^x + C2e^3x + C3e^(-2x).

The particular integral

for the function

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formula:

(e^2x + 3)^2 = e^4x + 6e^2x + 9 is obtainedby using the operator

1/P(D) which gives

1/P(D)e^4x = (e^4x)/18 , 1/P(D)e^2x = - (e^2x)/4 , 1/P(D)9 = 3/2.

Then the solution of the equation is

y = C1e^x + C2e^3x + C3e^(-2x) + (e^4x)/18 - (e^2x)/4 +3/2 .

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