If u2x2-y2-z2-1 then u- x- u- x-

The correct option is D 0 u=1√(x^2+y^2+z^2) xdudx= x^2(x^2+y^2+z^2)^3/2 ydudy= y^2(x^2+y^2+z^2)^3/2 zdudz= z^2(x^2+y^2+z^2)^3/2 ∑ xdudz ...

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Degree of a Differential Equations

If u2x2+y2+...

Question

If $u^{2} (x^{2} + y^{2} + z^{2}) = 1$ then $u + \sum x \frac{\partial u}{\partial x} =$

u^{- 3 / 2}

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\frac{5}{2} u^{- 5 / 2}

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Solution

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u = f (r), r^{2} = x^{2} + y^{2}

\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} = f (r) + \frac{2}{r} f^{'} (r)

u = f (r), r^{2} = x^{2} + y^{2} + z^{2}

\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} + \frac{\partial^{2} u}{\partial z^{2}} = f (r) + \frac{1}{r} f^{'} (r)

u = f (r)

r^{2} = x^{2} + y^{2} + z^{2}

\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} + \frac{\partial^{2} u}{\partial z^{2}} = f^{''} (r) + \frac{2}{r} f (r)

u = \frac{1}{\sqrt{x^{2} + y^{2} + z^{2}}}

x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} + z \frac{\partial u}{\partial z} =

y = t a n (\frac{1}{2} c o s^{- 1} \frac{1 - u^{2}}{1 + u^{2}} + \frac{1}{2} s i n^{- 1} \frac{2 u}{1 + u^{2}})

x = \frac{2 u}{1 - u^{2}}

\frac{d y}{d x}

u = a x^{2} + 2 h x y + b y^{2}

x \frac{\partial^{2} u}{\partial x \partial y} + y \frac{\partial^{2} u}{\partial y^{2}} = ?

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