Question

Consider the following PDE u_{xx} + 2u_{xy} - 3u_{yy} = 0 u(x, 0) = sin(x) u_{y}(x, 0) = x a) Reduce it into the canonical form b) Find the general solution c) Find the specific solution

          Consider the following PDE
u_{xx} + 2u_{xy} - 3u_{yy} = 0
u(x, 0) = sin(x)
u_{y}(x, 0) = x
a) Reduce it into the canonical form
b) Find the general solution
c) Find the specific solution

Added by Jorge N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Qbs Educator

04/14/2022

Step 1

Therefore, the PDE is hyperbolic. The characteristic equation is given by \(\frac{dx}{1} = \pm \sqrt{B^2 - 4AC} = \pm \sqrt{-8} = \pm 2i\). So, the characteristic equations are \(x = s \pm 2t\) and \(y = t\). Let \(v(s, t) = u(x, y)\). Then, we Show more…

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Consider the following PDE u_{xx} + 2u_{xy} - 3u_{yy} = 0, u(x,0) = sin(x), u_y(x,0) = x. a) Reduce it into the canonical form b) Find the general solution c) Find the specific solution