Question

Use Euler's method to approximate the solution of the differential equation $y' = -4y + \frac{2t}{y}$ with initial condition $y(4) = 2$ on the interval $[4, 8]$ with 20 number of steps. $y(8) \approx$

          Use Euler's method to approximate the solution of the differential equation $y' = -4y + \frac{2t}{y}$ with initial condition $y(4) = 2$ on the interval $[4, 8]$ with 20 number of steps.
$y(8) \approx$
        
Use Euler's method to approximate the solution of the differential equation y' = -4y + (2t)/(y) with initial condition y(4) = 2 on the interval [4, 8] with 20 number of steps.
y(8) ≈

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Computer Science and Information Technology
Computer Science and Information Technology
Trishna Knowledge Systems 2018 Edition
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I need a Python code for the following problem. NOTE: SHOW WRITTEN WORK FOR CALCULATING Y1, Y2, & Y3. Use Euler's method to approximate the solution of the differential equation y' = 4y + - with initial condition y(4) = 2 on the interval [4, 8] with 20 number of steps. y(8)~
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Transcript

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00:01 Hi from the question given that, d -y by d x is equal to y minus 4x and y of 2 is equal to 0 and the value of h is equal to 0 .5.
00:24 Here we need to find the value of y1 comma, y2 comma, y3 comma y4 by using the oilers method.
00:37 In general we know that formula for x n plus 1 is equal to x n plus h and y n plus 1 equal to y n plus 1 equal to y n plus f of xn comma y n into h and the value of f of x comma y is equal to t x now substitute the values to find the result now substitute x not is equal to 2 and y not is equal to 0 therefore the value of x 1 is equal to 2 .5 and the value of y 1 is equal to y not plus f of x0 comma y0 into h so this is equal to 0 plus f of 2 .0 into half.
01:44 So after simplifying this we obtain the value will be minus 4.
01:48 Therefore the value of y1 is equal to minus 4.
01:55 Now we need to find the value of y2.
01:59 So x2 is equal to 3.
02:02 Therefore y2 is equal to y 1 plus f of x1 comma y1 into h.
02:12 Similarly, we get minus 4 plus f of 5 by 2 that is 2 .5 comma minus 4 into half that is 0 .5 can be related as half so after simplifying this we obtained the value will be minus 11 that is the value of y2 will be equal to minus 11 now the value of x3 is equal to 7 by 2.
02:46 Similarly, y3 is equal to y2 plus f of x2 comma y2 into h...
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