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Sane

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Given the two equations:

[tex]y(1) = \pi[/tex]

[tex]\frac{dy}{dx} = \frac{6x^{2}}{2y + \cos{y}}[/tex]

Solve for x:

[tex]\begin{align*}

\int(2y+\cos{y})dy &= \int(6x^{2})dx\\

y^{2} + \sin{y} &= 2x^{3}\\

\end{align*}[/tex]

But in order to set a value to the function y, I need some way to exclude y and then plug in 1 for x. How do I exclude y when it's in two separate terms?

Or is there an easier way to do this?

[tex]y(1) = \pi[/tex]

[tex]\frac{dy}{dx} = \frac{6x^{2}}{2y + \cos{y}}[/tex]

Solve for x:

[tex]\begin{align*}

\int(2y+\cos{y})dy &= \int(6x^{2})dx\\

y^{2} + \sin{y} &= 2x^{3}\\

\end{align*}[/tex]

But in order to set a value to the function y, I need some way to exclude y and then plug in 1 for x. How do I exclude y when it's in two separate terms?

Or is there an easier way to do this?

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