I know this question is a little bit of stretch but is there any way to shuffle terms in an equation set, making those equations written in a standard form?
For example, here are three equations:
eq1:=(L1/n12 + n12*L2)*diff(i2(t), t) + L1*diff(i3(t), t)/n13 = -v1(t) - R1*i3(t)/n13 - R1*i2(t)/n12 + n12*v2(t) - n12*R2*i2(t);
eq2:=L1*diff(i2(t), t)/n12 + (L1/n13 + n13*L3)*diff(i3(t), t) = -v1(t) - R1*i3(t)/n13 - R1*i2(t)/n12 + n13*v3(t) - n13*R3*i3(t);
eq3:=-L2*diff(i2(t), t) + L1*diff(i1(t), t)/n12 = -v2(t) + R2*i2(t) + v1(t)/n12 - R1*i1(t)/n12;
In this equation set, it can be inferred that 'i1(t)', 'i2(t)' and 'i3(t)' would be the state variables and 'v1(t)', 'v2(t)' and 'v3(t)' are external input variables.
Then, probably the set can be rewritten in the state space equation form, i.e., diff(X) = A*X + B*U, where X is the state variables vector and U is a vector of external input variables.
Is there any chance to make Maple to rewrite the equations in this way?
Thank you in advance.