Partial Differential Equations- Nonlinear, semilinear, quasilinear, etc.

[awesomesauce9596]

I have

1.] sqrt(Ux)*Uy +U= cos(y)

2.] Ux+Uy+xU^2= sin(xy)

3.] yUxx- sqrt(x)*Uxy+xU=e^y

4.] UyUxx+Uyy+sqrt(Uy)=0

I have that 1) is nonlinear, 2) semilinear 3)nonlinear and 4)quasilinear, but I am confused. Can you guys give me the better definitions of each and explain why they are what they are? Thanks!!

 

[stapel]

I have

1.] sqrt(Ux)*Uy +U= cos(y)

2.] Ux+Uy+xU^2= sin(xy)

3.] yUxx- sqrt(x)*Uxy+xU=e^y

4.] UyUxx+Uyy+sqrt(Uy)=0

What were the instructions? What are you supposed to be doing with these?

I have that 1) is nonlinear, 2) semilinear 3)nonlinear and 4)quasilinear, but I am confused.

You are "confused" about what, specifically? Please be complete. Thank you!

 

[awesomesauce9596]

What were the instructions? What are you supposed to be doing with these?


You are "confused" about what, specifically? Please be complete. Thank you!

The directions were to give the linearity classification of each, sorry about that!