Math/Calculus
posted by COFFEE .
Solve the initialvalue problem.
Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else? Thanks.
y''+4y'+6y=0, y(0)=2, y'(0)=4
r^2+4r+6=0, r=(4 +/ sqrt(164(1)(6))/2
r=2 +/ sqrt(2)*i , alpha = 2, beta = 2(sqrt(2))
y=e^2x*(c1*cos(sqrt(2))x+c2*sin(sqrt(2))x)
y(0)=1*(c1+0)=2, c1=2
y'=(1/2)e^2x*(c1*(sin(sqrt(2)))/sqrt(2)c2*(cos(sqrt(2)))/sqrt(2))
y'(0)=(1/2)(01/sqrt(2)*c2)=4
c2=2/sqrt(2)
y(x)=e^2x*(2cos(sqrt(2))x+(2/sqrt(2))sin(sqrt(x))x)
I don't follow the y', recheck it. How did you get the 1/2 coefficient?
I got it...thanks.
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