Question

Verify the following.
1) Solution x^2
+y^2=Cy

Differential Equation y'=(2xy)/(x^2-
y^2)

Answer 1

x^2+y^2=Cy
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(x^2+y^2=Cy)'

2x+2yy'=Cy'
solve for y'
2x=Cy'-2yy'
2x=y'(C-2y)
2x/(C-2y)=y'
y'=2x/(C-2y)

Answer 2

but C=(x^2+y^2)/y

Answer 3

\[y'=\frac{2x}{\frac{x^2+y^2}{y}-2y}\]

Answer 4

\[y'=\frac{2x}{\frac{x^2+y^2}{y}-2y}*\frac{y}{y}\]

Answer 5

\[y'=\frac{2xy}{x^2+y^2-2y^2}\]

Answer 6

\[y'=\frac{2xy}{x^2-y^2}\]

Answer 7

you always provide the most elaborate explanations. Thanks, myininaya :]

Answer 8

you're so sweet

Answer 9

wow!