Question

Using Euler's Method, find the value of y(0.1), given that dy/dx= 1+xy
with y(0)-2
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Answer 1

Answer:

hii

Step-by-step explanation:

please give me thanks Kritika...

Answer 2

Given:  $\frac{dy}{dx} = 1 + xy$ with $y(0) = 2$

To find: find the value of y(0.1) by using Euler's method.

explanation:

as the equation given to us,

                                 $\frac{dy}{dx} = 1+xy$

that can be written as,

                                 $f(x) = 1+xy$

by using euler's method

                                 $yi_{+1} = yi + f(xi, yi) h$

consider step size 0.1 by putting h = 0.1 in the method equation,

                                  $y_{i} = y_{o} + f(x_{o} )$×$h$

by putting here, [tex]x_{o} = 0 , y_{o}= 2 [/tex],

                                  $y_{1} = 2+f(0,2)$×$0.1$

                                  $y_{1} = 2+(1+0$×$2)$×$0.1$

                                  $y_{1} = 2+1$×$0.1$$= 2.01$

                                 $x_{1} = x_{o}+h = 0.1+0 = 0.1$

Hence the value of y(0.1) is $y_{1}$ = 2.01