Word Count : 204

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The differential equation is [ \frac{d^2 x}{dt^2} - 3 \frac{dx}{dt} - 10 x = 0, \quad x(0) = 1, \quad \dot{x}(0) = 0. ] Assume a solution of the form (x(t) = e^{rt}). Substituting gives the characteristic equation: [ r^2 - 3r - 10 = 0. ] Solve the quadratic: [ ___ ___ _________ _________ __________.
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