Given thecomplementary solution and the differential equation, Give theparticular and the total solution for the initial conditions.
Use C1 and C2 for theweights, where C1 is associated with the root with smallermagnitude. If the roots are complex, the complementary solution isthe weighted sum of complex conjugate exponentials, which can bewritten as a constant times a decaying exponential times a cosinewith phase. Use C1 for the constant and Phi for the phase. (Note:Some equations in the text give the constant multiplying thedecaying exponential as 2C1. This was done for the derivation. Theconstant for this problem should be C1 alone.)
(basically anythingwith a sin function will be marked as wrong by me)
y(0)=7y'(0)=2 Â Â
Given the differentialequationy′′+8y′+25y=2cos(1t+1.0472)u(t).
Complementary:(e^(-4*t)*(C1*cos(3*t+Phi)))*u(t)
