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Asked Nov 12, 2019
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2. Reduce the following second order PDES to canonical form.
-(1+y2u= 0
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2. Reduce the following second order PDES to canonical form. -(1+y2u= 0

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Expert Answer

Step 1

The given differential equation,

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-(1+y* ) u =0 xx

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Step 2

Check the given equation is hyperbolic, parabolic or elliptic.

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s2-4RT 0--4(1+ y?) 4(1-y)> This shows that the given equation is hyperbolic. of the given equation Find the roots -0 0+4(1+y2) 2 =(1+y2) That is 4-(1+y and 1+y?)

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Step 3

Find the characteris...

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--(1+y) (1+y2) and dx dy dy =-dx dx and (1+y2) (1+ y? tan yxc and tan" y =-x +c2 Assume the transformation tan yand 7 = tan y+x

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