xy^2+yx^2=1

i am not good at solving these problems.

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- Oct 16th 2008, 12:29 AMHandroimplicit differentiation
xy^2+yx^2=1

i am not good at solving these problems. - Oct 16th 2008, 12:34 AMPeritus
$\displaystyle

\begin{gathered}

xy^2 + yx^2 = 1 \hfill \\

\frac{d}

{{dx}}\left( {xy^2 + yx^2 = 1} \right) \hfill \\

\Rightarrow y^2 + 2xyy' + 2xy + x^2 y' = 0 \hfill \\

\end{gathered} $

all is left to do is isolate y', I hope you're good at this. - Oct 16th 2008, 12:53 AMticbol
x(y^2) +y(x^2) = 1

If it is with respect to x, or if you want dy/dx or y', then,

very basically,

[x(2y dy/dx) +(y^2)(1 dx/dx)] +[y(2x dx/dx) +(x^2)(1 dy/dx)] = 0

You see, "divide everything" by dx if it is with rexpect to x.

To continue,

[(2xy dy/dx ) +(y^2)] +[(2xy) +(x^2 dy/dx)] = 0

It does not have to be as slow as that. It's just mny way of explaining the basics or the details to you.

(2xy)y' +y^2 +2xy +(x^2)y' = 0

Collect the (y')s,

(2xy +x^2)y' = -2xy -y^2

x(2y +x)y' = -y(2x +y)

y' = -y(2x +y) / x(x +2y) -----------answer.