Question

If dy/dx = 7x^2/y^3 and y(3)=2, find an equation for y in terms of x

Answer 1

separate the variables might help:

dy/dx = 7x^2/y^3

(S) y^3 dy = (S) 7x^2 dx

(1/4) y^4 = (7/3)x^3 + C

y^4 = (28/3)x^3 + C

y = +- 4root[(28/3)x^3 + C]

maybe we can use logs to simplify??
)

Answer 2

e^(y^4) = e^[(28/3)x^3 + C]

e^4y = e^[(28/3)x^3] * e^C ; e^C is a constant.

Answer 3

ln both sides...
4y = C * (28/3)x^3

y = C * 28x^3/12

y = C * (7x^3)/3

is the best I get.... if its right :)

Answer 4

Ok I got it thanks!

Answer 5

you got the answer? if so, was I right?

Answer 6

Ya it was right

Answer 7

Yay!!! thanx :)