Question #108007
State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter example.
i) Equation cos(x+y)p + sin(x+y)q = z^2
is a quasi-linear equation.
ii) The solution of PDE
dz/dx + dz/dy =z^2 is z = -[y+f(x-y)]

Iii)(dz/dx)(dz/dy) - (dz/dy)^2 = 0
is a non-linear PDE.
1
Expert's answer
2020-04-07T11:11:10-0400

State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter example.

i) Equation cos(x+y)p + sin(x+y)q = z^2

is a quasi-linear equation.

ii) The solution of PDE

dz/dx + dz/dy =z^2 is z = -[y+f(x-y)]

Iii)(dz/dx)(dz/dy) - (dz/dy)^2 = 0

is a non-linear PDE.



1) True. It's linear with respect to the derivatives (p and q)

2)zx=f(xy);zy=1+f(xy)2) z_x=-f'(x-y); z_y=-1+f'(x-y)

zx+zy=1=/z2z_x+z_y=-1 {=}\mathllap{/\,} z ^ 2

False

3)True. It contains a nonlinear element (dzdy)2({dz\above{2pt} dy})^2



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