Question

1 solve dy/dx=e^×-y, y(o)=2 using taylor's
Series method upto 4th degree terms &
find the values of y (1.1)​

Answer 1

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Answer 2

Answer:

The value of y(1.1)=3.034

Step-by-step explanation:

Given y'=e^x-y, y(0)=2, h= 1.1

x(0)=1 and y(0)=1, h= 1.1

Differentiating successively,we get

y'= e^x-1

y''= e^x

y'''= e^x

y''''=e^x

Now substituting,we get

y'(0)= 1-1= 0

y''(0)= 1

y'''(0)= 1

y''''(0)= 1

Putting these values in Taylor's Series,we have

y(1.1)= y(0)+hy'(0)+(h^2/2!)y''(0)+(h^3/3!)y'''(0)+(h^4/4!)/y''''(0)= 1+0+(1.1)^2/2!+(1.1)^3/3!+(1.1)^4/4!= 1+1.12+0.67+0.244= 3.034

So, y(1.1)= 3.034