Transform the second-order differential equation \frac{d^{2} x}{d t^{2}}=3 x into a system of first-order differential equations.

Tobias Ali

Tobias Ali

Answered question

2021-07-05

Transform the second-order differential equation d2xdt2=3x into a system of first-order differential equations.

Answer & Explanation

Luvottoq

Luvottoq

Skilled2021-07-06Added 95 answers

Let dxdt=v (1), then we have
ddt(dxdt)=3x (d2xdt2=ddt(dxdt))
dvdt=3x (2)
From (1) and (2), we have the system
dxdt=0x+v
dvdt=3x+0v
[dxdtdvdt]=[0130][xv]

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