Answer:
y = Ae^2xcos√3 x + Be^2xsin√3 x
Step-by-step explanation:
Given the differential equation
y''-4y' +7y =0
Let my = y' and m²y =y''
The auxiliary equation is expressed as;
m²y - 4my +7y = 0
(m²-4m+7)y =0
Divide through by y;
m²-4m+7= 0
Factorize the auxiliary equation
m = 4±√16-4(7)/2
m = 4±√-12/2
m = 4±2√3 i/2
m = 2+√3i
From the complex number a = 2(real part)
b = √3 (imaginary part)
Substitute into the general solution
y = Ae^axcosbx + Be^axsinbx
y = Ae^2xcos√3 x + Be^2xsin√3 x
