Numerical Analysis Euler's Method

[mayaitagaki]

Please help me with this problem! I have no clue. I know how to deal with only dy/dx. But this includes dy/dx and dz/dx...
Please see the attachment :)

Step size h = 0.2
range x = 0 to 1
y(0) = 2
z(0) = 4

Thank you,
Maya

 

[vela]

What don't you get?

 

[HallsofIvy]

Just do two Euler calculations.

Since the d.e. are
[tex]\frac{dy}{dx}= -2y+ 4e^{-x}[/tex]
and
[tex]\frac{dz}{dx}= -\frac{yz^2}{3}[/tex]

use the given initial values x= 0, y= 2, and z= 4 to calculate the two right sides:
[tex]\frac{dy}{dx}= -2(2)+ 4e^{0}= -4+ 4= 0[/tex]
and
[tex]\frac{dz}{dx} -\frac{(2)(16){3}= \frac{32/3}= -10.66666...

Since h= .2, x= 0+ h= 0+ .2= .2, y= 2+ (dy/dx)h= 2 - 0= 2, z= 4+ (dz/dx)h= 4- 2.133333= 1.8666668.

and repeat.

 

[mayaitagaki]

thanks sooooo much! I've got it!