I need some help solving the differential equation y′′′=x+y y(1)=3 y′(1)=2 y′′(1)=1 and h=0.5 with Euler's method

pramrok62 2022-09-30 Answered
I need some help solving the differential equation
y = x + y y ( 1 ) = 3 y ( 1 ) = 2 y ( 1 ) = 1
and h=0.5 with Euler's method

I don't know how to rewrite the equation to a system of equations of the first order..
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Answers (1)

Farbwolkenw
Answered 2022-10-01 Author has 6 answers
Here is how you linearize the system, we are given:
y ( x ) = x + y , y ( 1 ) = 3 , y ( 1 ) = 2 , y ( 1 ) = 1
We can proceed as follows:
x 1 = y x 1 = y = x 2
x 2 = y x 2 = y = x 3
x 3 = y x 3 = y = x + y = x + x 1
So, our new system is:
x 1 = x 2 x 2 = x 3 x 3 = x + x 1
Note, the given initial conditions, similarly follow as:
y ( 1 ) = 3 x 1 ( 1 ) = 3
y ( 1 ) = 2 x 2 ( 1 ) = 2
y ( 1 ) = 1 x 3 ( 1 ) = 1
Now, apply Euler's method to this system using h = 0.5.
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