$\"\"$

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Euler $\"\"$ s method :

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Approximate values for the solution of the initial-value problem $\"\"$ $\"\"$ and $\"\"$ with step size $\"\"$ is

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$\"\"$ .

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$\"\"$

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The step size of the Euler $\"\"$ s method is $\"\"$ .

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Initial value problem is $\"\"$ and $\"\"$ .

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Compare the above initial value problem with general first-order initial problem.

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General first-order initial problem : $\"\"$ and $\"\"$ .

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Here $\"\"$ and $\"\"$ . Find the valuues $\"\"$ and $\"\"$ .

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Use the formula $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Find the valuues $\"\"$ and $\"\"$ .

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Substitute $\"\"$ , $\"\"$ in $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ , $\"\"$ in $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ , $\"\"$ in $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ , $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ , $\"\"$ , $\"\"$ , and $\"\"$ .