anonymous
  • anonymous
given y>0 and dy/dx=3x^2+4x/y. if the point (1,sqrt{10}) is on the graph relating x and y, then what is y when x=0?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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myininaya
  • myininaya
do you know to find y given y'?
anonymous
  • anonymous
dy/dx
anonymous
  • anonymous
?

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myininaya
  • myininaya
you have to integrate y' to get y
myininaya
  • myininaya
oh wait
myininaya
  • myininaya
i didn't see that other y
myininaya
  • myininaya
is it \[y'=\frac{3x^2+4x}{y} ?\]
anonymous
  • anonymous
yes
myininaya
  • myininaya
ok do you know separation of variables?
anonymous
  • anonymous
quotient rule product rule ?
myininaya
  • myininaya
\[\frac{dy}{dx}=\frac{3x^2+4x}{y}\] you want y so we need to integrate but before we do that we need to separate our y's from our x's
myininaya
  • myininaya
\[y dy=(3x^2+4x) dx\]
anonymous
  • anonymous
oh yes i know how to do that
myininaya
  • myininaya
i multiplied y on both sides and I multiplied dx on both sides now we need to integrate both sides
myininaya
  • myininaya
\[\int\limits_{}^{}y dy=\int\limits_{}^{}(3x^2+4x) dx\]
anonymous
  • anonymous
whats that long thing u just put
myininaya
  • myininaya
\[\frac{y^2}{2}=\frac{3x^3}{3}+\frac{4x^2}{2}+C\] whenever you integrate you need to do +C
anonymous
  • anonymous
i havent learned that thing yet
myininaya
  • myininaya
its the only way
myininaya
  • myininaya
what about finding the antiderivative?
myininaya
  • myininaya
do you know what that means?
anonymous
  • anonymous
i learned that friday
anonymous
  • anonymous
yes
myininaya
  • myininaya
thats with weird symbol means
myininaya
  • myininaya
what*
anonymous
  • anonymous
but i dont think i can use that symbol yet
myininaya
  • myininaya
hmmm... that's weird to me
anonymous
  • anonymous
oh :/
anonymous
  • anonymous
its fine i guess i should skip that problem and just ask the teacher 2morrow. ill put up a new one.
myininaya
  • myininaya
ok but that is all i did was found the antiderivative of both sides with respect to whatever varaible was in d( )
anonymous
  • anonymous
oh okay thanks either way :)
myininaya
  • myininaya
np

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