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August 23, 2014

August 23, 2014

Posted by **jhony** on Tuesday, April 10, 2012 at 11:44am.

a) the function f(x)=3/2 +cx^-2 is a solution of the differential equation xy'+2y=3

b) the differential equation dy/dx= (f(x)g(y))/ (F(x)+G(y) is separable.

- calculus -
**Steve**, Tuesday, April 10, 2012 at 3:42pma)

y=3/2 + c/x^2

y' = -2c/x^3

xy' + 2y = x(-2c/x^3) + 2(3/2 + c/x^2)

= -2c/x^2 + 3 + 2c/x^2 = 3

b)

dy/dx = f(x)g(y)/(F(x)+G(y))

dy/g(y) (F(x)+G(y)) = f(x)dx

There's no way to separate the variables. That pesky F(x) is stuck fast to dy, or G(y) is stuck to dx.

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