solve this differential equation.
asked Apr 4, 2016 in Calculus Answers by AB

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1 Answer

(d^2q/dx^2)+9(dq/dx)+81q=14.40 what is the value of q?

Auxiliary equation:   m^2 + 9m + 81 = 0

Solving this with the quadratic formuka gives: m = -(9/)2 ± (9/2)√3

From these two solutions of the auxiliary eqn the complimentary solution is given by,

qc = e^(-9/2){A.cos((9/2)√3.x) + B.sin ((9/2)√3.x)}

The particular solution is very obviously

qp = 14.40/81 = 8/45

The general solution is: qg = qc + qp

i.e. q(x) = e^(-9/2){A.cos((9/2)√3.x) + B.sin ((9/2)√3.x)} + 8/45

answered Apr 4, 2016 by Fermat Level 10 User (69,640 points)
edited Apr 4, 2016 by Fermat
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