State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example.
(1) Equation cos(x+y) p+sin(x+y) q=z^2+z is a quasi -linear equation.
(2) The solution of PDE dz/dx+dz/dy=z^2 is z=-[y+f(x-y) ].
(3) dz/dx.dz/dy-(dz/dy) ^2=0is a non -linear PDE.
1
Expert's answer
2020-03-16T11:07:47-0400
1) True. It's linear with respect to the derivatives (p and q)
2)"z_x=-f'(x-y);z_y=-1+f'(x-y)"
"z_x+z_y=-1\\ne z^2"
False
3)True. It contains a nonlinear element "(\\frac{dz}{dy})^2"
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