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<h1>
<p><em><strong>Euler Method .</strong></em> </h></p>
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<em>Q1.</em> Find the value of y at x = 0.4, for <em><span class="math inline">(<em>d</em><em>y</em>/<em>d</em><em>x</em>)+2<em>x</em><em>y</em><sup>2</sup> = 0</span></em> : y(0) = 1, h = 0.2 by using Euler method.
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<h1 id="solution">Solution :</h1>
<h2 id="we-know-that---x00.0-y01">We Know that -       <strong>x<sub>0</sub>=0.0 , y<sub>0</sub>=1</strong></h2>
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<h2>
y<sub>n+1</sub>=y<sub>n</sub>+h <em>f</em> (x<sub>n</sub>,y<sub>n</sub>)
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<h3 id="step-1-using-the-above-equation-we-know"><span style="color:blue"> Step 1:</span> Using the above equation we know<br></h3>
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y <sub>1</sub>=y<sub>0</sub>+h <em>f</em> (x<sub>0</sub>,y<sub>0 </sub>)
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<th>x<sub>0</sub></th>
<th>y<sub>0</sub></th>
<th>f(x<sub>0</sub>,y<sub>0</sub>)</th>
<th>x<sub>1</sub>=x<sub>0</sub>+h</th>
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<td>x<sub>0</sub>=0.000</td>
<td>y<sub>0</sub>=1.000</td>
<td>y<sub>1</sub>=1.000</td>
<td>x<sub>1</sub>=0.2</td>
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<h3 id="step-2we-know"><span style="color:blue"> Step 2:</span>We know</h3>
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y <sub>2</sub>=y<sub>1</sub>+h <em>f</em> (x<sub>1</sub>,y<sub>1 </sub>)
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<tr class="header">
<th>x<sub>1</sub></th>
<th>y<sub>1</sub></th>
<th>f(x<sub>1</sub>,y<sub>1</sub>)</th>
<th>x<sub>2</sub>=x<sub>1</sub>+h</th>
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<td>x<sub>1</sub>=0.2</td>
<td>y<sub>1</sub>=1.000</td>
<td>y<sub>2</sub>=.9200</td>
<td>x<sub>2</sub>=0.4</td>
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<h1 id="so-y0.4.9200-is-the-answer-of-the-equation.">So <span class="math inline"><em>y</em>(0.4)=.9200</span> is the answer of the equation.</h1>
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