1. Can someone help me solve the following system of differential equations? <mtable columnalig

Kyla Ayers

Kyla Ayers

Answered question

2022-06-08

1. Can someone help me solve the following system of differential equations?
d P 0 d t = C 1 λ P 0 P 1 + C 1 2 P 1 2 d P 1 d t = C 2 P 1 + C 1 λ P 0 P 1 1 2 ( 1 + λ ) C 1 P 1 2 + C 1 P 1 P 2 d P 2 d t = C 2 P 1 + C 1 2 λ P 1 2 C 1 P 1 P 2
2. (Extending above) Suppose we have K first order non-linear differential equations (similar to above), is there any simple method to solve them analytically?

Answer & Explanation

Eli Shaffer

Eli Shaffer

Beginner2022-06-09Added 16 answers

1. If you will summarize all three equations, you get
d P 0 d t + d P 1 d t + d P 2 d t = 0 ,
and therefore,
d ( P 0 + P 1 + P 2 ) d t = 0 ,
and therefore,
P 0 + P 1 + P 2 = C ,
where C is some constant.
Try now to substitute, say, P 0 = C P 1 P 2 to your system. Simplifying the expressions you will get the (algebraic, but not differential) dependence between P 1 and P 2 . Substituting this dependence again, you will obtain one ODE of the first order, which will be easy to solve.
oleifere45

oleifere45

Beginner2022-06-10Added 3 answers

2. According to your second question. The answer is negative. There is no any general method to deal with non-linear problems, since the structure of them can be very diverse and complex.

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