Question

find the general solution of the DE \[y\prime + {y \over x-2} = 5(x-2)y^{1\over 2}\]

Answer 1

\[y \prime+(y/(x-2))=5(x-2)\sqrt{y}\]
Is this the DE? If so I'll solve it giving you the solution with step by step explanation I'll scan it and will attach it...

Answer 2

Yes, that is correct. I can recognize it as a bernoulli equation but am stuck after that

Answer 3

Divide by sqrt(y) on LHS and RHS
\[{1 \over \sqrt{y}}{dy \over dx} + {y^{1/2} \over (x-2)}= (5-x)\]

Take
\[y^{1/2} = t\]
\[{1 \over 2y^{1/2}}{dy \over dx}={dt \over dx}\]
\[{1 \over y^{1/2}}{dy \over dx}={2*dt \over dx}\]

Now
\[2*{dt \over dx} + {t \over (x-2)} = 5-x\]
\[{dt \over dx} + {t \over 2(x-2)} = {(5-x)/ 2}\]
Now proceed normal way

Answer 4

At the end after solving the DE, substitute t=y^(1/2) back

Answer 5

@gmer , any problem/doubt??

Answer 6

Sorry it took so long I couldn't use my scanner b/c it's hooked wireless to another computer, which someone else in the house was using to watch netflix...they weren't so happy I interrupted their movie =/ to scan math docs...