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chwala

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- Homework Statement
- Find the solutions satisfying ##2u_x-6u_y=0## given ##u(0,y)=\sin y##.

- Relevant Equations
- method of characteristics

Looking at pde today- your insight is welcome...

##η=-6x-2y##

therefore,

##u(x,y)=f(-6x-2y)##

applying the initial condition ##u(0,y)=\sin y##; we shall have

##\sin y = u(0,y)=f(-2y)##

##f(z)=\sin \left[\dfrac{-z}{2}\right]##

##u(x,y)=\sin \left[\dfrac{6x+2y}{2}\right]##

##η=-6x-2y##

therefore,

##u(x,y)=f(-6x-2y)##

applying the initial condition ##u(0,y)=\sin y##; we shall have

##\sin y = u(0,y)=f(-2y)##

##f(z)=\sin \left[\dfrac{-z}{2}\right]##

##u(x,y)=\sin \left[\dfrac{6x+2y}{2}\right]##

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