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Solve D Y D X = X . Y with Help of Euler’S Method ,Given that Y(0)=1 and Find Y When X=0.3 (Take H=0.1) - Applied Mathematics 2

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Sum

Solve `dy/dx=x.y` with help of Euler’s method ,given that y(0)=1 and find y when x=0.3
(Take h=0.1)

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Solution

`dy/dx=x.y=f(x,y)`   `x_0=0,  y_0=1`

`y_n=y_(n-1)+h.f(x_(n-1), y_(n-1))`

Iteration (n) `x_n` `y_n` `f(x_n,y_y)` `y_n+1=y_n+h.f(x_n,y_n)`
0 0 1 0 1
1 0.1 1 0.1 1.01
2 0.2 1.01 0.202 1.0302

∴y(0.3)=1.0302

Concept: Euler’S Method
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