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2 Systems of Differential Equations     continued...

Most computer codes for solving IVPs accept problems in the form (10). However, problems often arise in different forms. For example, one is often interested in solving the second order equation,

with initial conditions , . Here there is one unknown function from which we can, in principle, obtain . A new problem can be formed that involves two unknown quantities, and , but which is in the form (10). The idea is to identify independently by and by . Some manipulation then shows that and satisfy the system,

with