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solve:
\[ x\; {\partial z \over \partial x} + y\; {\partial z \over \partial y} = z \]
that passes though \( x^2+y^2+z^2=25 \) and \( x+y=1 \)
 one year ago
 one year ago
solve: \[ x\; {\partial z \over \partial x} + y\; {\partial z \over \partial y} = z \] that passes though \( x^2+y^2+z^2=25 \) and \( x+y=1 \)
 one year ago
 one year ago

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experimentXBest ResponseYou've already chosen the best response.0
the answer according to book is \[ 25(x+y) = x^2+y^2+z^2\] looks like intersection of two surfaces more than solution of DE
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
the solution looks like this ...
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
what kind of surface is that ... man i thought it would be a circle.
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
man how can we solve something like this? from the \(x^2+y^2+z^2=25\) we have \[{\partial z \over \partial x}=\frac{x}{z}\]\[{\partial z \over \partial y}=\frac{y}{z}\]put back in the original equation\[x^2+y^2=z^2\]lol
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
i'm supposed to do it by charpit's method ... an charpit's method is supposed to be easy than lagrange's method ... lol
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
i exactly did the same thing and got the same result!! x^2+y^2+z^2=0 !!
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
but this is wrong because it gives x=y=z=0
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
The lagrange method works ... but this is too ugly ... I have to eliminate z from 4th order equation
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
this is my last problem from first order DE ... I'm moving on to second order DE after this Q http://www.mathresources.com/products/mathresource/maa/charpits_method.html
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
man i cant get that answer with charpit
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
@experimentX santosh where are u....lol
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
still here man ... fishing answer from another site.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
what did you get for answer? i got z = a x + phi(a) y + c
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
had been doing \[ z = k_1x+k_2y+k_3 \]
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
k2 should be some function of k1 ... i guess there it would reduce my trouble by half
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
man let me try again..
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
let me try it again too
 one year ago

ValpeyBest ResponseYou've already chosen the best response.0
The intersection of the sphere and the plane will be a curve. The equation of the curve will solve \[x^2+(1x)^2+z^2=25\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
I need to find the particular integral of the given DE passing through both of these curves.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
no luck ... can't find \( \phi(k_1) \)
 one year ago

ValpeyBest ResponseYou've already chosen the best response.0
\[ \frac{\partial z}{\partial{x}}=\frac{2x2(1x)}{2z}=\frac{2x1}{z}\]Similarly solve for y and \[ \frac{\partial y}{\partial{z}}\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
and substitute it there?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
Looks like I messed up with Lagrange sol ... it didn't seem that difficult \[z/x = \phi(y/x)\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
the problem reduced to \[ z = ax +by \\ x^2+y^2+z^2=25\\ x+y=1\] Need to eliminate 'a' and 'b' from these equations.
 one year ago
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