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- #1

#### karush

##### Well-known member

- Jan 31, 2012

- 2,928

$${a}^{2}{u}_{xx}={u}_{t}$$

Is

$$u=\left(\pi/t\right)^{1/2}e^{{-x^2 }/{4a^2 t}}, \ \ t>0 $$

A solution to the differential equation

$${u}_{xx }$$

Was kinda hard to get, the TI-NSPIRE returned a very complicated answer

and it doesn't look like the differential equation is true