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experimentX
Group Title
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 \( x+y=1 \)
 2 years ago
 2 years ago
experimentX Group Title
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 \( x+y=1 \)
 2 years ago
 2 years ago

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experimentX Group TitleBest 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
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
the solution looks like this ...
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
what kind of surface is that ... man i thought it would be a circle.
 2 years ago

mukushla Group TitleBest 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
 2 years ago

experimentX Group TitleBest 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
 2 years ago

hartnn Group TitleBest 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 !!
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
but this is wrong because it gives x=y=z=0
 2 years ago

experimentX Group TitleBest 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
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
man i cant get that answer with charpit
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
@experimentX santosh where are u....lol
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
still here man ... fishing answer from another site.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
what did you get for answer? i got z = a x + phi(a) y + c
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
had been doing \[ z = k_1x+k_2y+k_3 \]
 2 years ago

experimentX Group TitleBest 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
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
man let me try again..
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
let me try it again too
 2 years ago

Valpey Group TitleBest 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 \[x^2+(1x)^2+z^2=25\]
 2 years ago

experimentX Group TitleBest 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.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
no luck ... can't find \( \phi(k_1) \)
 2 years ago

Valpey Group TitleBest 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 \[ \frac{\partial y}{\partial{z}}\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
and substitute it there?
 2 years ago

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

experimentX Group TitleBest 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.
 2 years ago
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