Question

Am I doing a step size for DE correctly?
(made up my own example)

Answer 1

With the following Differential Equation: \(\large\displaystyle\frac{dy}{dx}=x^2+2y\)
given that y(0)=1, what is y(8) ?

Answer 2

wait, I forgot the formula for step size...

Answer 3

hey, can you start me with the first step, with stepsize 1 ?

Answer 4

(stepsize, h=1 )

Answer 5

are you doing eulers method

Answer 6

Yes.

ok, I am really not sure, but I will try.

I am given a point (0,1)
the slope at this point is 0^2+2(1) = 2
So, my next point is:
(0+1 , 1 * 2 * 1)
(1,2)

Answer 7

is this correct?

Answer 8

it should be
(1, 1 + 1*2) = (1,3)

Answer 9

y sub (n-1) + (dy/dx at the point of y sub (n-1) ) * (step size) = y(sub n)

?

Answer 10

$$
\Large \rm {
\frac{dy}{dx}= f(x,y)\\
y_{n+1}= y_n + h \cdot f_n
\\~\\
\\ y_0 = 1
\\ y_1 = 1 + 1\cdot f_0= 1 + 1\cdot f(0,1)= 1 + 1\cdot 2 = 3
}
$$

Answer 11

y(2)=2 + 1*(1^2 + 2*2) = 2 + 1*(5) = 7

Answer 12

oh, the very first 2 should be a 3

Answer 13

then y(2)=8

Answer 14

then
y(3)=8+1*(2^2 + 2*3)=8+10=18

Answer 15

don't know why I am struggling, but tnx for taking your time to help me. I will read my book more.

Answer 16

All I needed is \(\displaystyle \Large \rm y_n=y_{n-1}+h~F(x_{n-1},y_{n-1})\) tnx again

Answer 17

y(2)=3 + 1*(1^2 + 2*3) = 3+7 = 10