General solution for given y'(x) = 2/(7-4y)

AI Thread Summary
To solve the differential equation y'(x) = 2/(7-4y), the method of separating variables is recommended. This involves rearranging the equation to (7-4y)dy = 2dx and integrating both sides. The integration yields the equation 7y - 2y² = 2x + k, which can be treated as a quadratic equation in y. By applying the quadratic formula, the general solution can be derived as y = 7/4 ± √(k - x). This approach effectively leads to the desired solution format.
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could some1 help me with the working of this question. it's for homework and i would help if i knew how to come to the answer in the back of the book.

it says to find the general solution (y=...)

given y'(x) = 2/(7-4y)

...


how do u get to this:
y = 7/4 +/- √(k-x)

that is: seven over four plus or minus the squareroot of k minus x

k being another constant

please help if u can

thanx
 
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Surely your textbook (not to mention your teacher!) has talked about "separating variables"!

y'= 2/(7- 4y) is the same as \frac{dy}{dx}= \frac{2}{7-4y}

"Separate" that into differential form with y on one side of the equation and x on the other:
(7- 4y)dy= 2dx.
Integrating: 7y-2y2= 2x+ k.

Now think of that as the quadratic equation 2y2- 7y+ (2x+k)= 0 and solve for y using the quadratic formula. (The "C" in Ay2+ By+ C is 2x+k.)
 
thank you very much

this is a great forum

very responsive
 

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