Question

Solve this DE: x(dy/dx)=1/(y^3)

Answer 1

\[y^3dy=\frac1xdx\]

Answer 2

\[x\frac{dy}{dx} = \frac{1}{y^3}\]
multiply by y^3, multiply by dx and divide by x to get:
\[y^3dy = \frac{1}{x}dx\]
Now, as if by magic, integrate!
\[\displaystyle\int y^3dy = \displaystyle\int x^{-1}dx\]
and remember your +C

Answer 3

\[\int\limits y^3dy=\int\limits \frac 1xdx\]
\[\frac {y^4}4=\ln x+c\]
\[y=(\ln x^4+c)^{1/4}\]

Answer 4

OOh thanks for the +C reminder or else i was trying to cancel out the exponent.. X_X

Answer 5

\[y(x) = \left(4\ln x + 4c\right)^{\frac{1}{4}}\] and let \[4c = C \in \mathbb{R}\]