Monday

April 21, 2014

April 21, 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.

**Related Questions**

calculus - Determine whether the statement is true or false. If it is true, ...

mathematics - Determine whether the statement is true, false, or sometimes true...

Math - Determine whether the statement is true, false, or sometimes true. ...

math - Find the value of the missing digit that makes the statement true. 214,...

calc - Determine whether the statement is true or false. d dx |x2 + x| = |2x + 1...

Geometry - Tell whether each statement is true or false. Then write the converse...

Math - Determine whether the statement is true or false. Show or explain why. If...

Math - Determine whether the statement is true or false. Show or explain why. If...

math - Indicate whether each statement is true or false by checking the ...

math - Determine whether the statement is true, false, or sometimes true. ...