du/dt = d2u/dx2(adsbygoogle = window.adsbygoogle || []).push({});

u(x,t) = (t^a) * (g(e)) where e = x/sqrt(t) and a is a constant

Show that

integral from -inf to inf [ u(x,t) ] dx = integral from -inf to inf [ (t^a) * g(e) ] dx

is independent of t only if a=-0.5

My attempt was to diff both sides by t (sorry not x) giving

integral from -inf to inf [d2u/dx2 ] dx = integral from -inf to inf [at^(a-1) g(e) + t^a dg(g)/dt ] dx

Not sure if this is correct and cant see where to go from here...any help most appreciated. Thanks

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# Show integral is independent

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