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?

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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
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do you know to find y given y'?
dy/dx
?

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Other answers:

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

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