SAGE : Laplace Transforms

Find the Laplace Transform for the following:

  1. $f(x)=c$
  2. $f(x)=x$
  3. $f(x)=x^2$
  4. $f(x)=x^n$
  5. $f(x)=e^{ax}$
  6. $f(x)=sin(ax)$
  7. $f(x)=cos(ax)$
  8. $f(x)=e^{a x}cos(bx)$
  9. $y'(x)$
  10. $y''(x)$

Inverse Laplace Transforms

Find the Inverse Laplace Transform for:

  1. $\frac{3s}{4-s}$
  2. $\frac{3s-4}{s^2-5s+6}$
  3. $\frac{3}{s^2-4s+13}$