Consider the differential equation dy/dx = xy. Let y = f(x) be the function that satisfies the differential equation with initial condition f(1) = 1. Use Euler's Method, starting at x = 1 with a step size of .1, to approximate f(1.2).

Question

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Respuesta :

okpalawalter8 okpalawalter8 · Answer 1 · 2021-01-27T03:11:38+01:00

Answer:

[tex]f(1.2)=1.221[/tex]

Step-by-step explanation:

From the question we are told that

[tex]dy/dx = xy[/tex]

Initial condition[tex]f(1) = 1.[/tex]

[tex]x = 1[/tex]

[tex]Step\ Size\ of\ 0.1[/tex]

Generally equation for [tex]y_1[/tex] is given mathematically as

[tex]f_0=F(1,1)=1[/tex]

Therefore

[tex]y_1=y_0+hf_0[/tex]

[tex]y_1=y_0+(0.1)(1)[/tex]

[tex]y_1=1.1[/tex]

Generally the approximation of the solution is mathematically given by

[tex]x=1+h\\x=1+0.1\\x=1.1[/tex]

[tex]y=1.1[/tex]

Generally the [tex]f_1[/tex] is mathematically given by

[tex]F_1=f(1.1,1.1)\\F_1=1.21[/tex]

Generally the [tex]y_2[/tex] is mathematically given by

[tex]y_2=y_1+hf_1\\y_2=1.1+0.121\\y_2=1.221[/tex]

Generally the approximation to the solution

at

[tex]y_2=1.221[/tex]

[tex]x_2=1.1+0.1\\x_2=1.2[/tex]

Therefore

[tex]f(1.2)=1.221[/tex]