Question

Use numerical techniques to solve the fallowing boundary value problem over the intercal from x=0 to 1.

dy/dx=(1+2x)*sqrt(y)

y(0)=1
Preferably I would like to be able to use MATLAB to find the answer, but I will take any help.

Answer 1

which numerical techniques do you know?

Answer 2

right now we are studying analytical solution, shooting method of derivative boundary conditions and nonlinear ODE's, also Finite-difference aproximation.

Answer 3

@SithsAndGiggles

Answer 4

Can't this be solved like any other separable equation? I'm not sure myself, since I have little experience in BVP's, but that's my first instinct on this question.

Answer 5

it can be solve by separable method, but I got y = [(x+x^2)^2 +c]/4 and don't know how to do next

Answer 6

@Loser66, I get \(y=\dfrac{(x^2+x+2)^2}{4}\) as a solution.

But if @NickChio6 is looking for a numerical approach, I'm afraid I can't be any help there.

Answer 7

That is what I am getting too, but I am not sure how to use that in a shooting method.

Answer 8

@oldrin.bataku

Answer 9

http://nm.mathforcollege.com/topics/shooting_method.html

Answer 10

you're missing your other boundary condition... what is it?

Answer 11

That is all the information I am given.

Answer 12

@loser66 When you have y = [(x+x^2)^2 +c]/4, you can use the boundary condition to determine c. You know that y(0)=1, filling this in should give you c.

Answer 13

@NickChio6 you need \(y(1)\)
@TimSmit not what he's talking about sorry