- #1

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## Main Question or Discussion Point

Hi,

I'm looking over the examples in my book for this problem and the general approach is

a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z)

where u(x,y)

I have the following problem in my notes:

1/x * u_x + 1/y * u_y = x^2 * sqrt(z)

and I get the solution easily because of the format:

Another problem i did was

y*u_x - x * u_y = 2xyu

where i multiplied both sides by 1/xy to get:

1/x*u_x - 1/y * u_y = 2u

the solution followed easily because of the classic format:

however, what i don't get is this format

u*u_x + y*u_y = x

the problem is an ivp with the following characteristics:

x = s, y = s, u = 2s

z = u(x_o,y_o) = u(s,s) = 2s

how do i get the solutin when it's not in the standard format? Or am i misinterpreting

a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z)

in the sense that the coefficient functions (a(x,y,z), b(x,y,z), c(x.y,z) can be any variable x,y,u(x_o,y_o)?

I don't have the book and all my examples are written in the convenient form i'm after which confuses me

thank you

I'm looking over the examples in my book for this problem and the general approach is

a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z)

where u(x,y)

I have the following problem in my notes:

1/x * u_x + 1/y * u_y = x^2 * sqrt(z)

and I get the solution easily because of the format:

Another problem i did was

y*u_x - x * u_y = 2xyu

where i multiplied both sides by 1/xy to get:

1/x*u_x - 1/y * u_y = 2u

the solution followed easily because of the classic format:

however, what i don't get is this format

u*u_x + y*u_y = x

the problem is an ivp with the following characteristics:

x = s, y = s, u = 2s

z = u(x_o,y_o) = u(s,s) = 2s

how do i get the solutin when it's not in the standard format? Or am i misinterpreting

a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z)

in the sense that the coefficient functions (a(x,y,z), b(x,y,z), c(x.y,z) can be any variable x,y,u(x_o,y_o)?

I don't have the book and all my examples are written in the convenient form i'm after which confuses me

thank you