- #1
jimagnus
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IVP Laplace Transform Problem -- Tricky Inverse Laplace Transform
Solve x"+x'+x=1, given x(0)=x'(0)=0
Plugged in transforms: s2*Y(s)-s*y(0)-y'(0)+s*Y(s)-y(0)+Y(s)=1/s
Plugged in initial value points, simplified to Y(s)=1/((s2+s+1)*s)
Partial Fractions led me to Y(s)=1/s+ (-s-1)/(s^2+s+1)
I get stuck at finding an inverse transform for the second term. You can't complete the square for the denominator, right?
Homework Statement
Solve x"+x'+x=1, given x(0)=x'(0)=0
Homework Equations
The Attempt at a Solution
Plugged in transforms: s2*Y(s)-s*y(0)-y'(0)+s*Y(s)-y(0)+Y(s)=1/s
Plugged in initial value points, simplified to Y(s)=1/((s2+s+1)*s)
Partial Fractions led me to Y(s)=1/s+ (-s-1)/(s^2+s+1)
I get stuck at finding an inverse transform for the second term. You can't complete the square for the denominator, right?