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How do you convert second order differential equations to first order differential equations?

In: Differential Equations [Edit categories]

Answer:

You can't convert a second order DE to first order except in special cases (like an ODE with y'' and y' but no y terms).

HOWEVER, you can convert a second order ODE into a system of first order ODEs:
Assume it is of the form f(x, y, y', y'') = 0, where y(x) is the solution.
1) Let u₁ = y and u₂ = y'
2) Substitute y'' for u₂', y' for u₂, and y for u₁ to get eq1
3) u₂ = u₁' is eq2.

eq1 and eq2 are a system of two first-order ODEs which represent the same problem.

First answer by Frrixxz. Last edit by Frrixxz. Contributor trust: 8 [recommend contributor ]. Question popularity: 26 [recommend question].

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