Basic PDE Solving

Calculus Level 2

Which of the following is not a function f ( x , t ) f(x,t) which satisfies the following first-order partial differential equation:

t ∂ t f = x ∂ x f ? t\partial_t f = x\partial_x f?

f ( x , t ) = x t f(x,t) = xt f ( x , t ) = x + t f(x,t) = x+t f ( x , t ) = x 2 t 2 f(x,t) = x^2 t^2 f ( x , t ) = e i x t f(x,t) = e^{ixt}

Matt DeCross by Matt DeCross , 27, USA

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1 solution

Matt DeCross
Mar 11, 2016

Each answer can be separately checked. Note that:

∂ t ( x + t ) = 1 = ∂ x ( x + t ) , \partial_t (x+t) = 1 = \partial_x (x+t),

so t ∂ t f = t ≠ x = x ∂ x f . t\partial_t f = t \neq x = x\partial_x f.

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