# calculus

posted by .

Solve the DE by using the Laplace transform:

x''+x=cos(3t), x(0)=x'(0)=0

• calculus -

L{x"} = s^2*F(s) - s*f(0) - f'(0)
= s^2*F(s)

so,

s^2 F(s) + F(s) = s/(s^2+9)

F(s) = s/((s^2+9)(s^2+1))
= 1/8 (s/(s^2+1) - s/(s^2+9))

f(t) = 1/8 (cos(t) - cos(3t))

check:
x' = 1/8 (3sin(3t)-sin(t))
x" = 1/8 (9cos(3t)-cos(t))

x'+x = 1/8 (8cos(3t)) = cos(3t)

## Similar Questions

what is the Laplace transform of e^4t(cos 2t) ?
2. ### college math

the Laplace transform of e^4t(cos 2t)?? please i need help. thanks
3. ### Calculus-HELP!!!

Find the Laplace transform of: f(t) = cos^(2)(2t)
4. ### Calculus-HELP!!!

Find the Laplace transform of: f(t) = cos^(2)(2t)
5. ### Calculus

Find the Laplace transform of: f(t)=t-2e^(3t)
6. ### Calculus-HELP!!!

Find the inverse Laplace transform of: F(s)=2/s^4
7. ### Calculus

Find the inverse Laplace transform of: F(s)=3/(s-4)
8. ### Calc2

Let f(t) be a function defined for all values of t. The Laplace Transform of f(t) is defined by: F(s)= ç[∘,‡](e^-st(f(t))dt). If the improper integral exists, Find the Laplace Transform for F(t)=t^2.
9. ### calc 2

(last one) ... Let f(t) be a function defined for all values of t. The Laplace Transform of f(t) is defined by: F(s)= ç[∘,‡](e^-st(f(t))dt). If the improper integral exists, Find the Laplace Transform for f(t)= sinhat
10. ### math

solve y"+4y-4z'=3x z"+z-y'=1-x where y(0)=z(0)=1 and y'(0)=z'(0)=0 by laplace transform

More Similar Questions