Unformatted text preview: 1. This is a second order PDE because of the u xx term. 2. This equation is linear. (Note that x and t are independent variables, so the x 2 doesn’t matter.) 3. To verify this, we simply plug in and see if it works: LHS: u t =x 2 et . RHS:x 2 2 u xx = x 2 2 · 2 et =x 2 et , so the LHS=RHS, so we have a solution....
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 Fall '07
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 Math, Differential Equations, Equations, Derivative, TA, x2 uxx

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