Hi everyone! Can anyone confirm my answer of y=1/4x^2 + 2x +c for the DE dy/dx=2+root(y-2x+3) and use a u-substitution of u=y-2x+3...Thanks! :o)

Question

anonymous · Answer

@ganeshie8

perl · Answer

is this the problem?
$$

\Large \frac{dy}{dx}= 2 + \sqrt{y-2x + 3}

$$

anonymous · Answer

@perl yes...sorry, got tied up for awhile

michele_laino · Answer

I got this general integral:
$$y\left( x \right) = \frac{{{{\left( {x + c} \right)}^2}}}{2} + 2x - 3$$

anonymous · Answer

hmmm...you don't have your work handy do you?
The reason I ask is because I worked this twice and got the same answer...
I very well could be wrong but I'm not 100% sure your answer is correct either

michele_laino · Answer

oops...:
$$y\left( x \right) = {\left( {\frac{{x + c}}{2}} \right)^2} + 2x - 3$$

michele_laino · Answer

using your substitution, I get:
$$u' = \sqrt u $$

michele_laino · Answer

so, integrating once, I can write:
$$2\sqrt u  = x + c$$

anonymous · Answer

yikes...I had this problem on my whiteboard and erased it! :o/
I will work it again on paper and post it if you have time to compare it with your work?

michele_laino · Answer

ok!

anonymous · Answer

thanks! :o)
brb

anonymous · Answer

One of the way to confirm: if y = 1/4 x^2 +2x +c is solution , then
                                              y' =........
consider given y'= 2+root(y -2x+3), replace y above into it, if it is  = y' we calculate above, then we are correct. |dw:1425390861731:dw|