SOLUTION: please any one solve this differential equation : (2ax+x^2)dy/dx=a^2+2ax

Question 964019: please any one solve this differential equation :
(2ax+x^2)dy/dx=a^2+2ax
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

If the numerator were the derivative of the denominator, we
would be able to integrate using
The derivative of the denominator is 2a+2x.
The numerator a+2x only needs to have "a" added to it to become that
So in the numerator we will add "a" and subtract "a"

Write as the difference of two fractions and integrate each:

Use the natural log formula on the first integral, and take the
constant "a" outside the second integral:

To the side, let's complete the square in the denominator by
adding and subtrracting a²:

To do the remaining integral we use the formula

Edwin
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