Question: How do I solve a system of non-linear equations (some of which are homogenous of degree 1)?

Dear Maple community,

I was wondering whether you could help me with the following problem: Consider the non-linear system of 4 equations in 4 unknowns: {y[2,1], y[2,2], y[4,1], y[4,2]}, see Please also note that equations y[2,1] and y[2,2] in sys2 are homogenous of degree 1 (i.e., defined only up to scale). In principle, it should be possible to choose either y[2,1] or y[2,2] as a free and unconstrained variable (a scaling factor) and express all other unknowns in terms of it. Unfortunately, I couldn't yet implement it in the current setting and was wondering whether you give me a hand. Thank you very much in advance!


sys1 := {y[4, 1] = 33^(2/3)*50^(1/3)/(33*(1/(y[2, 1]^(3/2)*y[4, 1]^(3/2)))^(1/3))+2^(2/3)*5^(1/3)/(2*(1/(y[2, 2]^(3/2)*y[4, 2]^(3/2)))^(1/3)), y[4, 2] = 11^(2/3)*50^(1/3)/(11*(1/(y[2, 1]^(3/2)*y[4, 1]^(3/2)))^(1/3))+4^(2/3)*5^(1/3)/(4*(1/(y[2, 2]^(3/2)*y[4, 2]^(3/2)))^(1/3))}

sys2 := {y[2, 1] = 33/(100*sqrt(y[2, 1])*y[4, 1]^(3/2)*(33/(50*y[2, 1]^(3/2)*y[4, 1]^(3/2))+2/(5*y[2, 2]^(3/2)*y[4, 2]^(3/2))))+11/(40*sqrt(y[2, 1])*y[4, 1]^(3/2)*(11/(20*y[2, 1]^(3/2)*y[4, 1]^(3/2))+1/(2*y[2, 2]^(3/2)*y[4, 2]^(3/2))))+3*y[2, 2]/(20*y[2, 1]^(3/2)*y[4, 1]^(3/2)*(11/(50*y[2, 1]^(3/2)*y[4, 1]^(3/2))+4/(5*y[2, 2]^(3/2)*y[4, 2]^(3/2))))+3*y[2, 2]/(10*y[2, 1]^(3/2)*y[4, 1]^(3/2)*(11/(25*y[2, 1]^(3/2)*y[4, 1]^(3/2))+3/(5*y[2, 2]^(3/2)*y[4, 2]^(3/2)))), y[2, 2] = 11*y[2, 1]/(75*y[2, 2]^(3/2)*y[4, 2]^(3/2)*(33/(50*y[2, 1]^(3/2)*y[4, 1]^(3/2))+2/(5*y[2, 2]^(3/2)*y[4, 2]^(3/2))))+11*y[2, 1]/(60*y[2, 2]^(3/2)*y[4, 2]^(3/2)*(11/(20*y[2, 1]^(3/2)*y[4, 1]^(3/2))+1/(2*y[2, 2]^(3/2)*y[4, 2]^(3/2))))+2/(5*sqrt(y[2, 2])*y[4, 2]^(3/2)*(11/(50*y[2, 1]^(3/2)*y[4, 1]^(3/2))+4/(5*y[2, 2]^(3/2)*y[4, 2]^(3/2))))+3/(10*sqrt(y[2, 2])*y[4, 2]^(3/2)*(11/(25*y[2, 1]^(3/2)*y[4, 1]^(3/2))+3/(5*y[2, 2]^(3/2)*y[4, 2]^(3/2))))}



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