$1.$

$(35$ points$)$

Use the shooting method to solve

the Boundary Value P

roblem

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$2$

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$2$

$+$

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$=$

$2$

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$,$

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$($

$0$

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$=$

$1,$

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$2$

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$8.$

Us

e the midpoint method with

step size

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$=$

$0\mathrm{.}4$

to solve the system of ODEs