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Question Number 168977 by MikeH last updated on 23/Apr/22
$check that the function u(x,t) = exp{−((n^2 α^2 π^2 )/L^2 )t} sin((nπx)/L) n = 1,2,... satisfy the heat equation heat equation α^2 (∂^2 u/∂x^2 ) = (∂u/∂t), 0 < x < L$
$check that the function$ $u (x, t) = \exp {- \frac{n^{2} α^{2} π^{2}}{L^{2}} t} \sin \frac{n π x}{L}$ $n = 1, 2, . . . satisfy the heat equation$ $heat equation$ $α^{2} \frac{\partial^{2} u}{\partial x^{2}} = \frac{\partial u}{\partial t}, 0 < x < L$
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