MATLAB: How solve two symbolic non-linear equations

equationnonlinearnonlinear equationsolvesymbolicsymbolic nonlinear equation

I wrote this code to solve equations1 and 2 in terms of variables (ILm and Vo)
syms ILm Vo IL Vin  Ip1 Ip2 Ip3 Is1 Is2 Is3 T3 T4 %%%variables
syms Vin Lk1 Lk2 n k Lm D T R T1 T2 %%%constants
Ip1=(1-k)*Vin*T1/Lk1-(n*IL-ILm)/(n+1);
Ip2=(1-k)*Vin*D*T/Lk1-(n*IL-ILm)/(n+1);
Ip3=(n*IL-ILm)/(n+1);
Is1=Vin*(1+n*k)*T1/Lk2-(IL+ILm)/(n+1);
Is2=Vin*(1+n*k)*D*T/Lk2-(IL+ILm)/(n+1);
Is3=(IL+ILm)/(n+1);
T3=D*T*Vin/(Vo-2*Vin);
T4=(1-D)*T-T3;
IL=Vo^2/(Vin*R);
eq1=-T3*(Is2+Ip2+IL)*0.5+0.5*(Ip3^2*Lk1/(Vin-k*Vin)-Ip1*(T1-Ip3*Lk1/(Vin-k*Vin))+Is3^2*Lk2/(Vin+n*k*Vin)-(T1-Is3*Lk2/(Vin+Vin*n*k))*Is1)-0.5*T2*(Is1+Is2+Ip1+Ip2)+T3*.5*(IL-Is2-Ip2)+IL*T4;
eq2=-Vo*T/R+0.5*(Is3^2*Lk2/(Vin+n*Vin*k)-Is1*(T1-Is3*Lk2/(Vin+n*k*Vin)))-0.5*(Is1+Is2)*T2-0.5*(Is2^2*Lk2/((1+n*k)*(Vo-2*Vin)))+Is3*0.25*(T3-Is2*Lk2/((1+n*k)*(Vo-2*Vin)))+Is3*T4;
[Voans ILmans]=solve([eq1,eq2],[Vo ILm])
but i get this:
solutions might be lost!
Can anyone help me which part i am doing wrong?

Best Answer

You are not doing anything wrong. You are just asking for something more complicated than it can solve without further help.
If you solve(eq1, Vo) then it will give you three root() expressions -- that is, Vo is the three roots of a cubic. Notice that the roots do not involve the variable ILm.
Now solve(eq2, ILm) and see that it gives two solutions (it is a quadratic), and that those solutions do involve Vo.
The overall solution is therefore to take solve(eq2, Ilm) and substitute in each of the three values for Vo in turn, producing a total of 6 solutions.
These overall full solutions will be of essentially no use to you, as they go on for pages and pages and are pretty much impossible for any human to make any intuitive sense of.
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