Question: (10 points) Use Fourier transforms to derive a solution to the the initial value problem: F[e^(-ax^(2))](omega )=(1)/(sqrt(4pi a))e^(-(omega ^(2))/(4a))u_(t)=tu_(times ),-infty 0 u(x,0)=f(x),-infty The formula F[e^(-ax^(2))](omega

(10 points) Use Fourier transforms to derive a solution to the the initial value problem: F[e^(-ax^(2))](\omega )=(1)/(\sqrt(4\pi a))e^(-(\omega ^(2))/(4a))u_(t)=tu_(\times ),-\infty 0 u(x,0)=f(x),-\infty The formula F[e^(-ax^(2))](\omega )=(1)/(\sqrt(4\pi a))e^(-(\omega ^(2))/(4a)) might be useful

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