Solve the differential equation

What I have done:

At this point I thought it would be best to factor out the x term.

Is my work so far correct? Looking at the left side I don't know what the next step is.

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- Jan 30th 2010, 10:38 AMEm Yeu AnhFirst order differential equation
Solve the differential equation

What I have done:

At this point I thought it would be best to factor out the x term.

Is my work so far correct? Looking at the left side I don't know what the next step is. - Jan 30th 2010, 11:36 AMGrandad
- Jan 30th 2010, 11:46 AMEm Yeu Anh
- Jan 30th 2010, 11:54 AMDefunkt
- Jan 30th 2010, 01:14 PMGrandad
- Jan 30th 2010, 01:41 PMCalculus26
My 2 cents:

An eqn like y ' + p(x) y = q(x) y^n

is an example of a Bernoulli equataion which can easily be solved

by letting v = y ^ (1-n)

http://www.mathhelpforum.com/math-he...182c7387-1.gif

or y ' -2xy = x y^2

is an example of a Bernoulli equataion n = 1

Let v= y ^(-1)

dv/dx = -y^(-2)dy/dx

-y^2 dv/dx - 2xy = x y^2

dv/dx + 2x v = -x

Which can now be solved with the intergating factor e^(x^2)

d(ve^(x^2)) = -xe^(x^2)dx

v = -1/2 + ce^(-x^2)

y= 1/v = 1/ [-1/2 + ce^(-x^2)]