Answer to Question #91536 in Differential Equations for Sajid

Question

Q. Choose the correct answer.
Q. The equation u_xx 〖-4u〗_xy=0 is
)parabolic
b)hyperbolic
c)Elliptic
d) None of above

Answer 1

$$u_{xx} - 4u_{xy} =0$$

The equation

$$A u_{xx}+2 B u_{xy} + C u_{yy} + D u_{x} + E u_{y} + F =0$$

is elliptic if

$$AC-B^2 >0$$

hyperbolic if

$$AC - B^2 <0$$

and parabolic if

$$AC - B^2 =0$$

We have A = 1, B = -2, C =0, hence

$$1 \times 0 - (-2)^2 = -4<0$$

i.e. the answer is b) hyperbolic