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GATE EC 2010 Official Paper

Option 2 : 0.031

__Concept:__

Using Euler's first order method

\(\mathop y\nolimits_{n + 1} = \mathop y\nolimits_n + hf(\mathop x\nolimits_n ,\mathop y\nolimits_n )\)

**Analysis:**

Step size, h = 0.1

\(\rm y_1^p = y_0 + hf(x_0, y_0)\)

*\(\rm \frac{du(x)}{dx} - y(x) = x\)*

y = 0 ⇒ x = 0, h = 0.1

y = 0.3

\(\rm \frac{dy}{dx} = x + y\)

y_{1}_{ }= y_{0} + h(x_{0} + y_{0})

= 0 + 0.1 × 0 f(x_{0} y_{0}) = 0 + 0

y_{1} = 0

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

= 0 + 0.1 × [0.1 + 0]

= 0.01

y_{3} = y_{2} + 0.1 (x_{2} + y_{2})

= 0.01 + 0.1 (.2 + 0.01)

= 0.01 + 0.021

= 0.031