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

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

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
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
78,526 questions
82,365 answers
63,405 users