(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