MATH SOLVE

2 months ago

Q:
# Find the general solution of yʹ − 3y = 8e3t + 4sin t .

Accepted Solution

A:

Answer:y =[tex] C_1e^{3t}[/tex] + [tex] Ate^{3t}+ Bsint + Ccost[/tex]Step-by-step explanation:[tex]{y}^{'} - 3y = 8e^{3t} + 4 sin t[/tex][tex]\frac{\mathrm{d} y}{\mathrm{d} t} - 3y = 8e^{3t}+4sint[/tex]writing characteristic equation; ( m - 3 ) y = 0m = 3[tex]y = C_1e^{3t}[/tex]for particular solution [tex]y_p = Ate^{3t}+ Bsint + Ccost[/tex]hence general solution becomes y = C.F + P.Iy =[tex] C_1e^{3t}[/tex] + [tex] Ate^{3t}+ Bsint + Ccost[/tex]