I am given: y′′=11−y y(2)=1;y′(2)=−4 and asked to use Euler's method to find y(2.2) for h=0.1 To find y′ I simply took the integral of y′′ to get: y′=11x−yx However, this does not satisfy the condition given above, that y′(2)=−4. Is this not the correct way of obtaining the first order derivative?

Crancichhb 2022-08-14 Answered
y = 11 y
y ( 2 ) = 1 ; y ( 2 ) = 4
and asked to use Euler's method to find y ( 2.2 ) for h = 0.1
To find y I simply took the integral of y to get:
y = 11 x y x
However, this does not satisfy the condition given above, that y ( 2 ) = 4. Is this not the correct way of obtaining the first order derivative?
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Answers (1)

Jakob Chavez
Answered 2022-08-15 Author has 14 answers
The first-order system for your second-order equation is simply
y = v , v = 11 y ,
and the first Euler step correspondingly
y 1 = y 0 + h v 0 , v 1 = v 0 + h ( 11 y 0 ) .
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integral f'(x) = integral(x+1) *f(x)+(x+1) * integral (f(x)
so f(x) = ((x^2+x)/2)*f(x) + (x+1) * (f(x)^2)/2.
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asked 2022-08-22
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