Transform the given differential equation or system into an equivalent system of first-order differential equations. x^{(3)}=(x')^{2}+\cos x

nitraiddQ

nitraiddQ

Answered question

2021-05-01

Transform the given differential equation or system into an equivalent system of first-order differential equations.
x(3)=(x)2+cosx

Answer & Explanation

d2saint0

d2saint0

Skilled2021-05-02Added 89 answers

Consider the differential equation
x(3)=(x)2+cosx
The objective is to transform tha given differential equetion into an equivalent system of first-order differeential equations.The third-order equation
x(3)=(x)2+cosx
is equivalent to
f(t,x,x,x)=(x)2+cos2
Now, let's be
x=x1
x=x2=x1
x=x3=x2=x1
The above substitution yields the system as written below
x1=x2
x2=x3
x3=x22+cosx1
are the three first order differential equations.

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