$\"\"$

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The differential equation is $\"\"$ and intial condition $\"\"$ .

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The exact solution $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the above equation.

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$\"\"$

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Substitute $\"\"$

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$\"\"$

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Substitute $\"\"$

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$\"\"$

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Substitute $\"\"$

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$\"\"$

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Substitute $\"\"$

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$\"\"$

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Substitute $\"\"$

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$\"\"$

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$\"\"$

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Using eulers method.

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$\"\"$

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ , $\"\"$ in the above equation.

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$\"\"$

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ , $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in the above equation.

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$\"\"$

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\

\

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$\"\"$

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
\ $\"\"$ \ Exact \	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
\ $\"\"$ \ $\"\"$ \	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
\ $\"\"$ \ $\"\"$ \

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\