Question

If dy/dx = x * square root of (2x^2+1) , and y contains the point (2,4), then the y-intercept of the particular solution is A)0 B) -2/3 C)-1/3 D)-4/3 or E)-1?

Answer 1

Also here's the dy/dx equation typed out so it's easier to understand:\[dy/dx = x \sqrt{2x^2+1}\]

Answer 2

How far can you get on your own?

Answer 3

I usually understand the steps fairly well but I think making sure the variables are on the correct side and are distributed correctly is what's messing me up.

Answer 4

Show me your steps and I can correct you from there.

Answer 5

Okay so I did the integral of the following:\[1/y dy = x \sqrt{2x^2+1}\] and I got \[y =( x^2/2)(2/3(2x^2+1)^1.5)\] if that makes sense!

Answer 6

Where did the 1/y part come from? I got: \[\frac{dy}{dx} = x \sqrt{2x^2+1}\]\[\int\limits \frac{dy}{dx} dx = \int\limits x \sqrt{2x^2+1} dx\]\[y = \int\limits x \sqrt{2x^2+1} dx\] I think you are on the right track with your integral on the x side, I picked u=2x^2+1 so that meant du/dx=4x and got \[y=\frac{2}{3} \frac{1}{4}(2x^2+1)^{3/2}+C\]

Answer 7

Oh okay so you have to use u substitution! I think that's just the real step I was missing out on. Thanks!

Answer 8

Yeah, and you're good with the next step after this to find the particular solution from this general solution too?

Answer 9

Yeah I think so! Thanks again for your help :)!

Answer 10

Awesome, keep it up, sometimes substitution can be tricky so good luck and be clever!