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Solve the initial value problem:
x(dy/dx)+y(x) = 9y(x)^(2), y(1) = 1
 one year ago
 one year ago
Solve the initial value problem: x(dy/dx)+y(x) = 9y(x)^(2), y(1) = 1
 one year ago
 one year ago

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mathew0135Best ResponseYou've already chosen the best response.1
\[x \frac{ dy }{dx } + y(x) = 9y(x)^2 , y(1) =1\] Just the equation a little neater
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
I would solve for dy/dx and intergrate.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
the ex's int he brackets are just indicating the independent variable right?\[x \frac{ \text dy }{\text dx } + y = 9y^2 , \]
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
and we know y(1) = 1.
 one year ago

mathew0135Best ResponseYou've already chosen the best response.1
I believe so, that's just how its been written. I'll try solving for dy/dx and integrating then,
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
So I would sub those in.
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
u realize that you can separate the variables easily here ?
 one year ago

mathew0135Best ResponseYou've already chosen the best response.1
\[\frac{ dy }{ dx } = \frac{ 9y(x)^2y }{ x }\] Not too familiar with these problems, but basically i need to integrate that, no?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
u bring all terms of one variable on one side of = sign, like this : \(\large \frac{1}{9y^2y}dy=\frac{1}{x}dx\) then integrate
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
can u integrate both sides now ?
 one year ago

mathew0135Best ResponseYou've already chosen the best response.1
think i got it, left an x over the y side so i confused my self. \[1 = \ln(19y)\ln(y)\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
u integrated yvariable correctly , but what about \(\int (1/x)dx\) its not =1
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
i meant u should get something like this : \(\ln x=ln(19y)lny+c\) then use logarithmic properties to simplify
 one year ago

mathew0135Best ResponseYou've already chosen the best response.1
Okay, catching on think i figured out what i did wrong when i integrated last anyway.
 one year ago

mathew0135Best ResponseYou've already chosen the best response.1
Maybe y = \[\frac{ 1 }{ x+9 }\] May be a final solution, just simplifying the equation?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
ln cx= ln (19y)/y cxy= (19y) now use y(1) = 1 to find c.
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
u got this simplification ? >ln cx= ln (19y)/y
 one year ago

mathew0135Best ResponseYou've already chosen the best response.1
yup, \[C(1)(1)=19(1)\] \[C=10\] \[C=10\] \[10xy=(19y)\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
10xy =19y or 10xy9y+1=0
 one year ago

mathew0135Best ResponseYou've already chosen the best response.1
ahh, forgot the negative, think i have enough to try a few more of these questions any way. Thank you. :)
 one year ago
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