anonymous
  • anonymous
Solve this DE: x(dy/dx)=1/(y^3)
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[y^3dy=\frac1xdx\]
anonymous
  • anonymous
\[x\frac{dy}{dx} = \frac{1}{y^3}\] 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
anonymous
  • anonymous
\[\int\limits y^3dy=\int\limits \frac 1xdx\] \[\frac {y^4}4=\ln x+c\] \[y=(\ln x^4+c)^{1/4}\]

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anonymous
  • anonymous
OOh thanks for the +C reminder or else i was trying to cancel out the exponent.. X_X
anonymous
  • anonymous
\[y(x) = \left(4\ln x + 4c\right)^{\frac{1}{4}}\] and let \[4c = C \in \mathbb{R}\]

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