# How do you use the laplace transform to sovle this equation?

intergral from 0 to t f(r)f(t-r)dr=6t^3

How do u do this question. Some steps would be great. Thanks

Relevance
• Anonymous

intg[f(r).f(t-r)].dr from 0 ---> t is the convolution f * f by definition...

so take the laplace transform of both sides gives you;

F(s) . F(s) = 36/s^2

so F(s) = +/- 6/s^2

then take the inverse laplace of both sides to get;

f(t)=+/-6t