Question

dy/DX=1/x+y with y(0)=1 and step size h=0.1 then value of k1 as defined in Runge kutta method
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Answer 1

Given:

dy/dx = 1/x+y

y(0) = 1

h = 0.0

To find:

The value of k₁ as defined in the Runge Kutta method

Solution:

We have f(x,y) = 1/x+y

x₀ = 0

y₀ = 1

h = 0.1

k₁ = hf(x₀,y₀)

k₁ = 0.1f(0,1)

k₁ = 0.1 × (1/0+1)

k₁ = 0.1

Therefore, the value of k₁ is 0.1