Question

what is the general solution of the following differential equation....x^3 dy/dx=y^-4

Answer 1

\[x^3 \frac{dy}{dx} = y^{-4} \implies \frac{dy}{dx} = \frac{y^{-4}}{x^3} \implies \frac{dy}{y^{-4}} = \frac{dx}{x^3} \]Integrate both sides to get the general solution

Answer 2

In general, no. These are a special case of solving differential equations. You are trying to separate variables, with y and dy on one side and dx and x on the other. It's not necessarily true that doing something like this is feasible.

Answer 3

but the 2 questions so far..thats the approach i take rite??

Answer 4

Yeah. Like I said, it's a useful tool and many times you can solve using it. But don't try it always, always think before trying some (very likely) messy algebra.

Answer 5

okay...

Answer 6

can u show me the steps u did with this 1

Answer 7

integrating dy/y^-4=integral of dx/x^3...do u carry the exponents to the top?

Answer 8

Yeah. One is y^4 and the other is x^(-3). Use the power rule.

Answer 9

i dont get what u did..u divided by y^2 already??

Answer 10

? The integral of y^4 = (y^5)/5. Similarly, the integral of x^(-3) = (x^(-2))/(-2). And those dx should disappear.

Answer 11

No dy and no dx. And remember that there should be a +C after you finished calculating an anti-derivative.

Answer 12

okay i c what ur saying..thxx:)

Answer 13

No problem :-)