Solve this ODE using Laplace transforms
$$y'''(x) - 6y''(x) +11y'(x) - 6y (x) = g (x)$$ with $y (0) = 1 $ and $y'(0) = y''(0) = 0$
This is very strange. How do I solve this if $g (x)$ is unknown? I believe this requires convolution, but I don't know how to proceed after applying the laplace transforms.
Hint: the characteristics equation $$r^3-6r^2+11r-6=0$$ $$(r-1)(r-2)(r-3)-0$$ so the complementary solution is $$y_c=c_1e^x+c_2e^{2x}+c_3e^{3x}$$ then use the variation of parameters to find the general solution see