How Does a Linear System Respond to a Sine Wave Input Using Fourier Transform?

[jaguar515]

Find the response of the of the linear system at rest
y' + y = x , where x = sin(t)
using the Fourier transform and formulas :

Y(jw)=H(jw)X(jw)
y(t)=h(t)*x(t) convolution

 

[SGT]

Find the response of the of the linear system at rest
y' + y = x , where x = sin(t)
using the Fourier transform and formulas :

Y(jw)=H(jw)X(jw)
y(t)=h(t)*x(t) convolution

If the FT of y(t) is $$Y(j\omega)$$ what is the FT of y'(t)?