Suppose $x=c_1{e}^{-t}+c_2{e}^{3t}.$

a$.$ Verify that $x=c_1{e}^{-t}+c_2{e}^{3t}$ is a solution to $x^{\text{'}\text{'}}-2x^{\text{'}}-3x=0$ by substituting it into the differential equation. $($Enter the terms in the order given. Enter $c_1$ as $c1$ and $c_2$ as $c2.)$

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b$.$ Find $x(t)$ if $x(0)=5$ and $x^{\text{'}}(0)=3.$

$x(t)=$

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