54.2k views
1 vote
The given differential equation is. ( D 2 + 6 D + 10 ) y = 6 e − 3 θ cos ⁡ θ. The auxiliary equation is. m 2 + 6 m + 10 = 0 .

User Neelshiv
by
7.9k points

1 Answer

1 vote

Final answer:

The given differential equation is (D^2 + 6D + 10)y = 6e^(-3θ)cosθ. The solution to this equation involves solving the auxiliary equation, which yields complex roots. The general solution to the differential equation is y = e^(-3θ)(Acosθ + Bsinθ).

Step-by-step explanation:

The given differential equation is (D^2 + 6D + 10)y = 6e^(-3θ)cosθ. To find the solution, we need to solve the auxiliary equation m^2 + 6m + 10 = 0.

Using the quadratic formula, we can find the roots of the auxiliary equation: m = (-6 ± √(6^2 - 4*1*10))/(2*1) = -3 ± i.

Since we have complex roots, the general solution to the differential equation is y = e^(-3θ)(Acosθ + Bsinθ), where A and B are constants determined by the initial conditions.

User Patrick Tescher
by
8.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories