Math Archive: Questions from 2023-03-30

f(t) + 0 t(t - tau)f(tau)dtau = t Use the Laplace transform to solve the given integral equation.

1 answer

f(t) = 5t - 25 int 0 t sin(tau)f(t - tau)dtau Use Laplace transform to solve the given integral equation.

1 answer

f(t)= tet + int 0 t tau f(t - tau) dtau Use the Laplace transform to solve the given integral equation.

1 answer

f(t) + int 0 t f(tau) dtau = 2Use Laplace transform to solve the given integral equation.

1 answer

f(t) = cos(t) + int 0 t e^-tau f(t - tau) dtau Use Laplace transform to solve the given integral equation

1 answer

f(t) = 1 + t - 8/3 int 0 t (tau - t)^3 f(tau)dtau Use Laplace transform to solve the given integral equation

1 answer

y'(t) = 1 - sin(t) - int 0 t y(tau)dtau, y(0) = 0 Use the Laplace transform to solve the given differential equation.

1 answer