Question

The partial differential equation yuxx + Uyy = 0 is hyperbolic if a) y < 0 b) y > 0 c) y = 0 d) y = 0​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The partial differential equation

$\sf{yU_{xx} + U_{yy} = 0}$

is hyperbolic if

a) y < 0

b) y > 0

c) y = 0

d) y = 0

EVALUATION

Here the given partial differential equation is

$\sf{yU_{xx} + U_{yy} = 0}$

Comparing with the general equation

$\sf{aU_{xx} +bU_{xy} + c U_{yy} = 0}$

We get

a = y , b = 0 , c = 1

Now the given equation is hyperbolic

Thus we get

$\sf{ {b}^{2} - 4ac > 0 }$

$\sf{ \implies \: {0}^{2} - 4.y.1 > 0 }$

$\sf{ \implies \: - 4y > 0 }$

$\sf{ \implies \: y < 0 }$

FINAL ANSWER

Hence the correct option is a) y < 0

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