Transforming to a Normal Form (PDE)

[lema21]

Homework Statement

Find the type, transform to normal form and solve. Show your work in detail: Uxx+2Uxy+Uyy=0

Relevant Equations

Hyperbolic- AC-B^2<0
Parabolic- AC-B^2=0
Elliptic- AC-B^2>0

I don't know how to solve for u(x,y) from where I left of after 5.

 

[MathematicalPhysicist]

Shouldn't you be getting: $u_{ww}=0$, i.e. $u(w,v)=Aw+B(v)$ where $B(v)$ is a function of $v$ and $A$ is a constant?

 

[pasmith]

Shouldn't you be getting: $u_{ww}=0$, i.e. $u(w,v)=Aw+B(v)$ where $B(v)$ is a function of $v$ and $A$ is a constant?

The indefinite integral of $0$ with respect to $w$ is an arbitrary function of $v$, not an arbitrary ocnstant.

 

[MathematicalPhysicist]

The indefinite integral of $0$ with respect to $w$ is an arbitrary function of $v$, not an arbitrary ocnstant.

yes correct then A should be A(v).