system of two linear ordinary differential equations

Question

Abdullah 2012-3-1

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https://ww2.mathworks.cn/matlabcentral/answers/30774-system-of-two-linear-ordinary-differential-equations

Hello Everyone

I had a very difficult question, that we are required to solve it using either Matlab or Math-cad:

The question has been posted 5 hours ago, but the question was not clear nor the answer, the question is a system of two linear ordinary differential equations with symbolic constants, this is a picture of the question:

http://img842.imageshack.us/img842/7180/screenshot20120301at317.png

I already tried "Dsolve" and it did not work.

Can I solve this using Matlab ??!

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Answer 1

Kai Gehrs 2012-3-5

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在 MATLAB Online 中打开

Hi,

I think the system should be solvable without any issues. Here is the MATLAB code to solve the system and to verify the solutions using the Symbolic Math Toolbox:

syms a b c d;      
S= dsolve('Dx + y/(b*c) + (x*(a + b))/(a*b*c) = 0',...
          'Dy + x/(b*d) + y/(b*d) = 0',...
          'x(0)=1','y(0)=-1');
% verify solution for x      
simplify(diff(S.x) + S.y/(b*c) + (S.x*(a + b))/(a*b*c))
% verify x(0)=1
simplify(subs(S.x,0))
% verify solution for y
simplify(diff(S.y) + S.x/(b*d) + S.y/(b*d))
% verify y(0)=-1
simplify(subs(S.y,0))

Hope this helps and best regards,

-- Kai

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Valentina 2012-3-16

Hello Kai,

I've the same problem of Abdullah, but my system is much more complex. Please read my question at:

http://www.mathworks.it/matlabcentral/answers/32477-solve-a-differential-equations-system-with-dsolve

My system is composed by 5 differential equations plus a simple linear one without derivatives. Now I'm attempting to solve a simplifyed system with only 3 derivatives.

I wrote in Matlab (after having called my coefficients with letters from a to o):

syms x y z w

S = dsolve('Dx - y*c/e - x^3*y*b/e + x*b*Tamb^3/e - x^4*a/e + x^3*b/e + a/e*Tamb^4 + b/e*Tamb^3 + d/e=0',...

'Dy - z*f/m + y*a*Tamb^3/m + y*f/m + y/(m*g) - Y*i*l/m + x^3*y*a/m + x*a*Tamb^3/m - x^4*a/m + Tamb/(m*g) + h/m - i/m - i*l/m*T_ref=0',...

'Dz + w *n/o + z*f/o - y*f/o + n*Tf0/o=0',...

'w -z*2 +Tf0=0');

It doesn't work.

Thank you for your help.

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