anonymous
  • anonymous
Differential:solve for y yy'=y+sqrt(x^2+y^2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
i wonder, let y = vx y' = v'x + v might be useful
anonymous
  • anonymous
So originally i tried to do that and i got to
anonymous
  • anonymous
one second

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anonymous
  • anonymous
\[x \frac{ dv }{ dx }=1-v+\sqrt{\frac{ 1 }{ v^2 }+1}\]
anonymous
  • anonymous
from here would i try to do separable?
amistre64
  • amistre64
yy'=y+sqrt(x^2+y^2) vx(v'x+v)=vx+sqrt(x^2+v^2x^2) vv'x^2+v^2x = vx+x sqrt(1+v^2) v'+v/x = 1/x+ sqrt(1+v^2)/vx v' = 1/x+ sqrt(1+v^2)/vx - v/x v' = 1/x (1 + sqrt(1+v^2)/v - v) dv / (1 + sqrt(1+v^2)/v - v) = dx /x hmmm, can we make that left side any better?
amistre64
  • amistre64
\[\frac{v}{v-v^2+\sqrt{1+v^2}}dv=\frac1xdx\] im wondering of a conjugate would be useful .... these are just ideas, how useful they may be is anyones guess
anonymous
  • anonymous
alright sounds good..ill play with it for a little while and see what i get
amistre64
  • amistre64
burnooli comes to mind for non linear diffy Qs, but i cant say a recall much about it
amistre64
  • amistre64
i really do need to bruch up on my diffy Qs :)
anonymous
  • anonymous
Ehh bummers i'm not getting the "simple, clean" answer that they have written. I'll just go into office hours, but thank you for your help

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