- #1
squenshl
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Homework Statement
Find the general solution of the following equation
ut + x2ux = t, u(x,0) = f(x), -inf < x < inf, t > 0
Homework Equations
The Attempt at a Solution
Using method of characteristics I get
du/dt = ut + dX/dtux = ux(dX/dt - x^2) + t
so along the curve dX/dt = x^2 with x(0) = x0 we get x = -1/(t+x0) and x0 = -1/x - t
So du/dt = t = -1/x - x0 so
u(x,t) = -t/x - x0t + f(x0)
so u(x,t) = t2 + f(-1/x - t)
but when I check this I don't get the original PDE.
Someone help.