Write new boundary conditions to a system of ODEsSuppose we have the following system of equations:{x¨1=f(x1,x2)x¨2=g(x1,x2)x1(0)=αx2(0)=βx˙1(0)=γx˙2(0)=δwhere all the derivatives are made in a time variable t.Since I would like to work with a system of first order equations, I would go like this:{x˙1=x3x˙3=f(x1,x2,x3,x4)x˙2=x4x˙4=g(x1,x2,x3,x4)How can I apply the starting conditions at time t=0 at the new system?

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Ireland Huff · Accepted Answer

Your approach doesn&#039;t make much sense to me. How can the functions f and g depend on 2 variables, but after that, they depend on 4? I am not used to this kind of ODE notation, but seems to me, after you have introduced the variables x3=x˙1 and x4=x˙2, you just have to keep it consistent. Don&#039;t extend the functions f and g and just do simple symbolic substitution to the initial values and you should be fine.

Write new boundary conditions to a system of ODEs Suppose we have the following system of equati

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