1.y''+6y'=8
2.y'+ytgx=(cosx)^2
2.y'+ytgx=(cosx)^2
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2.) y' + (tan(x))*y = cos²(x)
Integrating factor = e^(∫tan(x) dx) = sec(x)
Multiplying both sides by integrating factor:
y'*sec(x) + (sec(x)*tan(x))*y = cos(x)
d/dx[y*sec(x)] = cos(x)
y*sec(x) = sin(x) + C
y = cos(x)*(sin(x) + C)
Integrating factor = e^(∫tan(x) dx) = sec(x)
Multiplying both sides by integrating factor:
y'*sec(x) + (sec(x)*tan(x))*y = cos(x)
d/dx[y*sec(x)] = cos(x)
y*sec(x) = sin(x) + C
y = cos(x)*(sin(x) + C)
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1)
y[x] = (4 x)/3 - 1/6 e^(-6 x) C[1] + C[2]
y[x] = (4 x)/3 - 1/6 e^(-6 x) C[1] + C[2]