Solving coupled Differential equations

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JaeSung Choi 2017-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/360701-solving-coupled-differential-equations

评论： JaeSung Choi 2017-10-15

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I tried to solve following diff. eq. using 'dsolve' but (maybe) it's impossible.

So please help me how to solve following eq.s using matlab!!!!!

syms s1 s2 s3 g1 g2 g3 p1 p2 p3 t
h = 1; b = 2; e = exp(1); v = 1;
diffqp1 = 'Dp1 = h*b*s1*(g1-p3)-(e/v)*p1'
diffqp2 = 'Dp2 = h*b*s1*(g1-p3)-(e/v)*p2'
diffqp3 = 'Dp3 = h*b*s1*(g1-p3)-(e/v)*p3'
diffqs1 = 'Ds1 = -h*b*s1*(g1-p3)-(e/v)*s1'
diffqs2 = 'Ds2 = -h*b*s1*(g1-p3)-(e/v)*s2'
diffqs3 = 'Ds3 = -h*b*s1*(g1-p3)-(e/v)*s3'

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Walter Roberson 2017-10-11

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Are your g1 g2 g3 functions or constants?
What boundary conditions are there?
you never use g2 or g3 but use g1 repeatedly

Presuming that g1 is a constant and not a function, then current syntax would look like

syms s1(t) s2(t) s3(t) g1 g2 g3 p1(t) p2(t) p3(t)
h = 1; b = 2; e = exp(1); v = 1;
Dp1 = diff(p1); Dp2 = diff(p2); Dp3 = diff(p3);
Ds1 = diff(s1); Ds2 = diff(s2); Ds3 = diff(s3);
diffqp1 = Dp1 == h*b*s1*(g1-p3)-(e/v)*p1;
diffqp2 = Dp2 == h*b*s1*(g1-p3)-(e/v)*p2;
diffqp3 = Dp3 == h*b*s1*(g1-p3)-(e/v)*p3;
diffqs1 = Ds1 == -h*b*s1*(g1-p3)-(e/v)*s1;
diffqs2 = Ds2 == -h*b*s1*(g1-p3)-(e/v)*s2;
diffqs3 = Ds3 == -h*b*s1*(g1-p3)-(e/v)*s3;
eqns = [diffqp1, diffqp2, diffqp3, diffqs1, diffqs2, diffqs3];
sol = dsolve(eqns);