Question

The value of first iterative root y1 = y(0.1) of y'+ 2y = 0, y(0) = 1, h = 0.1 i​

Answer 1

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product. Let's start by grouping the 5start color #11accd, 5, end color #11accd and the 4start color #11accd, 4, end color #11accd together.

Answer 2

Answer:

y₁=0.8, y₂=0.64

Step-by-step explanation:

Given y¹+2y=0

we rewrite as y¹=-2y, y(0)=1,

which is of the form of equation f(x,y)=-2y, x₀=0, and y₀=1

Euler's method yileds

y₁=y₀+hf(x₀,y₀)

  =1+(0.1)f(0,1)

  =1+(0.1)(-2)       since f(x,y)=-2y⇒f(0,1)=-2×1=-2×0.8=-1.6

  =1+(-0.2)=1-0.2

y₁   =0.8

y₂=y₁+hf(x₁,y₁)

   =0.8+(0.1)f(0.1,0.8)

  =0.8+0.1×-1.6       since,f(0.1,0.8)=-2

  =0.8-0.16

y₂=0.64

So the value y₁=0.8, y₂=0.64

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