Question

Given the complementary solution and the differential equation, Give the particular and the total solution for the initial conditions.

Use C1 and C2 for the weights, where C1 is associated with the root with smaller magnitude. If the roots are complex, the complementary solution is the weighted sum of complex conjugate exponentials, which can be written as a constant times a decaying exponential times a cosine with phase. Use C1 for the constant and Phi for the phase. (Note: Some equations in the text give the constant multiplying the decaying exponential as 2C1. This was done for the derivation. The constant for this problem should be C1 alone.)

(basically anything with a sin function will be marked as wrong by me)

y(0)=7 y'(0)=2   

Given the differential equation y′′+8y′+25y=2cos(1t+1.0472)u(t).

Complementary:(e^(-4*t)*(C1*cos(3*t+Phi)))*u(t)

Answer 1

NOTE: Ignore u(t) while solving differential equation