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khush77
10.03.2020 •
Mathematics
Suppose f is a function of one variable that has a continuous second derivative. Show that for any constants a and b, the function u(x,y) = f(ax + by) is a solution of the PDE uxxuyy −u2xy = 0.
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Ответ:
We can find the solution using chain rule,
For instance, if u(x,y) = f(ax+by), then
and then derivative of
with respect to y is
Now, the derivative of
with respect to x, which is the second derivative, which is
and the derivative
and
are
Finally, the solution of PDE is
= 0,
As the PDE is equal to 0, it means the function u(x,y) = f(ax+by) is the solution of the given PDE.
Ответ:
148
Step-by-step explanation: