exact solution for non linear first order ODEs

Hira Soomro

2021 6 16

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I wan to solve system of nonlinear first order odes to get the exact solution.

I am typing the code below in MATLAB which is giving this error. Can anyone please help to find where i am doing mistake (either typing or something else)

 syms y1(x) y2(x) y3(x)
Dy1=diff(y1(x));
Dy2=diff(y2(x));
Dy3=diff(y3(x));
Eqn1=Dy1==-1000*((power(y1(x),3)*power(y2(x),6))-power(cos(x),3)*power(sin(x),6))-sin(x);
Eqn2=Dy2==-1000*((power(y2(x),5)*power(y3(x),4))-power(sin(x),9))+cos(x);
Eqn3=Dy3==-1000*((power(y1(x),2)*power(y3(x),3))-power(cos(x),2)*power(sin(x),3))+cos(x);
[Y1,Y2,Y3]=dsolve(Eqn1,Eqn2,Eqn3,y1(0)==1,y2(0)==0,y3(0)==0);

Warning: Unable to find symbolic solution.

> In dsolve (line 209)

Can someone please help me how to write non linear equation in command window to find the exact solutions for system of equations.

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John D'Errico 2021-6-16

编辑：John D'Errico 2021-6-16

There is no assurance that an exact solution exists for nonlinear systems of differential equations (or any nonlinear equation in general.) DSOLVE has stated that it cannot find one. Just wanting magic to happen is not sufficient.