Applied Mathematics for Electrical Engineering (3130908)

Question-3c ( i )

BE | Semester-3 Winter-2019 | 26-11-2019

Q3) (c ( i ))

Using Euler’s method find $y (0.2)$ , given that $\frac{dy}{dx} = y - \frac{2 x}{y}; y (0) = 1$ taking $h = 0.1$ .

\frac{dy}{dx} = y - \frac{2 x}{y} = f (x, y)

Now,

y (0) = 1 \Rightarrow y_{0} = 1, x_{0} = 0

By Euler’s method :

y_{n + 1} = y_{n} + h [f (x_{n}, y_{n})]

Where,

x_{n} = x_{0} + n h, n = 0, 1, 2, 3, \dots

For,

n = 0

For,

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

y_{1} = y_{0} + h f (x_{0}, y_{0})

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

y_{1} = 1 + (0.1) (1 - \frac{2 (0)}{1})

y_{1} = 1.1

For,

n = 1

Now,

x_{2} = x_{0} + 2 h = 0 + 0.2 = 0.2

y_{2} = y_{1} + h f (x_{1}, y_{1})

y_{1} = 1.1 + (0.1) f (0.1, 1.1)

y_{1} = 1 + (0.1) (1.1 - \frac{2 (0.1)}{1.1})

y_{1} = 1.9182

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