Question

Find f(x) if y = f(x) satisfies
\frac(dy)(dx) = 45 yx^(14)
and the y -intercept of the curve y = f(x) is 3 .

Answer 1

\[\frac{ dy }{ dx }= 45yx ^{14}\]

Answer 2

isn't that stated in the proble,?

Answer 3

that's the question...

Answer 4

if it is... then it is separable and you can integrate

Answer 5

just do implicit differentiation?

Answer 6

no... separate and integrate...\[\frac{ dy }{ dx }= 45yx^{14} \Rightarrow \frac{ dy }{ y }=45x^{14}dx\]

Answer 7

does this make sense?

Answer 8

OH yeah now I remember. Thank you!

Answer 9

the initial condition will help you determine what the constant should be.

Answer 10

yeah I forgot to separate my variables, that was really helpful!