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Mrac [35]
4 years ago
10

Use Euler's method with step size 0.2 to estimate y(2), where y(x) is the solution of the initial-value problem y' = 2 − 3xy, y(

1) = 0. (Round your answer to four decimal places.)
Mathematics
1 answer:
Zepler [3.9K]4 years ago
6 0

Answer:

y_2=0.512

Step-by-step explanation:

We are given that

Step size=0.2

Initial value problem

y'=2-3xy

f(x,y)=2-3xy

y(1)=0

We have to find the value of y_2

Euler's method of approximation

y_{n+1)=y_n+hf(x_n,y_n)

We have y_0=0,x_0=1

Substitute the value then we get when n=1

y_1=y_0+hf(x_0,y_0)

y_1=0+(0.2)(2-3(1)(0))

y_1=0.4

x_1=x_0+h=1+0.2=1.2

y_2=y_1+hf(x_1,y_1)

y_2=0.4+0.2(2-3(1.2)(0.4))

y_2=0.4+0.2\times 0.56

y_2=0.4+0.112=0.512

y_2=0.512

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