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Question: non linear system of equation

Question:non linear system of equation

ishan_bhan 10 Maple
multiplication syntax 2dmath rootfinding fsolve
April 10 2022
2

eqs.mw

 

km := 0.1784124116e-1/(6.8*e-9)

0.1784124116e-1/(6.8*e-9)

 (1)

NULLNULL

kf := 3141.592654

3141.592654

 (2)

up := 10

10

 (3)

lw := 0.1e-1

0.1e-1

 (4)

  

eq1 := C1*C2*C3*C4(C1*R2*R3*R4+C2*R1*R3*R4+C3*R1*R2*R4+C4*R1*R2*R3) = 84

C1*C2*C3*C4(C1*R2*R3*R4+C2*R1*R3*R4+C3*R1*R2*R4+C4*R1*R2*R3) = 84

 (5)

eq2 := C1*C2*C3*C4(C1*C2*R3*R4+C1*C3*R2*R4+C1*C4*R2*R3+C2*C3*R1*R4+C2*C4*R1*R3+C3*C4*R1*R2) = 126

eq3 := C1*C2*C3*C4*(C1*C2*C3*R4+C1*C2*C4*R3+C1*C3*C4*R2+C2*C3*C4*R1) = 36

C1*C2*C3*C4*(C1*C2*C3*R4+C1*C2*C4*R3+C1*C3*C4*R2+C2*C3*C4*R1) = 36

 (6)

eq4 := -C1*C2*C3*C4*R1*R2*R3*R4*Rin+C1^2*C2^2*C3^2*C4^2 = 0

-C1*C2*C3*C4*R1*R2*R3*R4*Rin+C1^2*C2^2*C3^2*C4^2 = 0

 (7)

eq5 := C1*C2*C3*C4*(C1*C2*C3*R4+C1*C2*C4*R3+C1*C3*C4*R2+C2*C3*C4*R1)-Rin*C1^2*C2*C3*C4*R2*R3*R4-C1*C2^2*C3*C4*R1*R3*R4*Rin-C1*C2*C3^2*C4*R1*R2*R4*Rin-C1*C2*C3*C4^2*R1*R2*R3*Rin-C1*C2*C3*R1*R2*R3*R4-C1*C2*C4*R1*R2*R3*R4-C1*C3*C4*R1*R2*R3*R4-C2*C3*C4*R1*R2*R3*R4 = 0

C1*C2*C3*C4*(C1*C2*C3*R4+C1*C2*C4*R3+C1*C3*C4*R2+C2*C3*C4*R1)-Rin*C1^2*C2*C3*C4*R2*R3*R4-C1*C2^2*C3*C4*R1*R3*R4*Rin-C1*C2*C3^2*C4*R1*R2*R4*Rin-C1*C2*C3*C4^2*R1*R2*R3*Rin-C1*C2*C3*R1*R2*R3*R4-C1*C2*C4*R1*R2*R3*R4-C1*C3*C4*R1*R2*R3*R4-C2*C3*C4*R1*R2*R3*R4 = 0

 (8)

eq6 := C1*C2*C3*C4*(C1*C2*R3*R4+C1*C3*R2*R4+C1*C4*R2*R3+C2*C3*R1*R4+C2*C4*R1*R3+C3*C4*R1*R2)-C1^2*C2^2*C3*C4*R3*R4*Rin-C1^2*C2*C3^2*C4*R2*R4*Rin-C1^2*C2*C3*C4^2*R2*R3*Rin-C1*C2^2*C3^2*C4*R1*R4*Rin-C1*C2^2*C3*C4^2*R1*R3*Rin-C1*C2*C3^2*C4^2*R1*R2*Rin-C1^2*C2*C3*R2*R3*R4-C1^2*C2*C4*R2*R3*R4-C1^2*C3*C4*R2*R3*R4-C1*C2^2*C3*R1*R3*R4-C1*C2^2*C4*R1*R3*R4-C1*C2*C3^2*R1*R2*R4-C1*C2*C4^2*R1*R2*R3-C1*C3^2*C4*R1*R2*R4-C1*C3*C4^2*R1*R2*R3-C2^2*C3*C4*R1*R3*R4-C2*C3^2*C4*R1*R2*R4-C2*C3*C4^2*R1*R2*R3 = 0

C1*C2*C3*C4*(C1*C2*R3*R4+C1*C3*R2*R4+C1*C4*R2*R3+C2*C3*R1*R4+C2*C4*R1*R3+C3*C4*R1*R2)-C1^2*C2^2*C3*C4*R3*R4*Rin-C1^2*C2*C3^2*C4*R2*R4*Rin-C1^2*C2*C3*C4^2*R2*R3*Rin-C1*C2^2*C3^2*C4*R1*R4*Rin-C1*C2^2*C3*C4^2*R1*R3*Rin-C1*C2*C3^2*C4^2*R1*R2*Rin-C1^2*C2*C3*R2*R3*R4-C1^2*C2*C4*R2*R3*R4-C1^2*C3*C4*R2*R3*R4-C1*C2^2*C3*R1*R3*R4-C1*C2^2*C4*R1*R3*R4-C1*C2*C3^2*R1*R2*R4-C1*C2*C4^2*R1*R2*R3-C1*C3^2*C4*R1*R2*R4-C1*C3*C4^2*R1*R2*R3-C2^2*C3*C4*R1*R3*R4-C2*C3^2*C4*R1*R2*R4-C2*C3*C4^2*R1*R2*R3 = 0

 (9)

eq7 := C1*C2*C3*C4*(C1*R2*R3*R4+C2*R1*R3*R4+C3*R1*R2*R4+C4*R1*R2*R3)-C1^2*C2^2*C3^2*C4*R4*Rin-C1^2*C2^2*C3*C4^2*R3*Rin-C1^2*C2*C3^2*C4^2*R2*Rin-C1*C2^2*C3^2*C4^2*R1*Rin-C1^2*C2^2*C3*R3*R4-C1^2*C2^2*C4*R3*R4-C1^2*C2*C3^2*R2*R4-C1^2*C2*C4^2*R2*R3-C1^2*C3^2*C4*R2*R4-C1^2*C3*C4^2*R2*R3-C1*C2^2*C3^2*R1*R4-C1*C2^2*C4^2*R1*R3-C1*C3^2*C4^2*R1*R2-C2^2*C3^2*C4*R1*R4-C2^2*C3*C4^2*R1*R3-C2*C3^2*C4^2*R1*R2 = 0

C1*C2*C3*C4*(C1*R2*R3*R4+C2*R1*R3*R4+C3*R1*R2*R4+C4*R1*R2*R3)-C1^2*C2^2*C3^2*C4*R4*Rin-C1^2*C2^2*C3*C4^2*R3*Rin-C1^2*C2*C3^2*C4^2*R2*Rin-C1*C2^2*C3^2*C4^2*R1*Rin-C1^2*C2^2*C3*R3*R4-C1^2*C2^2*C4*R3*R4-C1^2*C2*C3^2*R2*R4-C1^2*C2*C4^2*R2*R3-C1^2*C3^2*C4*R2*R4-C1^2*C3*C4^2*R2*R3-C1*C2^2*C3^2*R1*R4-C1*C2^2*C4^2*R1*R3-C1*C3^2*C4^2*R1*R2-C2^2*C3^2*C4*R1*R4-C2^2*C3*C4^2*R1*R3-C2*C3^2*C4^2*R1*R2 = 0

 (10)

eq8 := -C1^2*C2^2*C3^2*C4^2*Rin+C1*C2*C3*C4*R1*R2*R3*R4-C1^2*C2^2*C3^2*R4-C1^2*C2^2*C4^2*R3-C1^2*C3^2*C4^2*R2-C2^2*C3^2*C4^2*R1 = 0

-C1^2*C2^2*C3^2*C4^2*Rin+C1*C2*C3*C4*R1*R2*R3*R4-C1^2*C2^2*C3^2*R4-C1^2*C2^2*C4^2*R3-C1^2*C3^2*C4^2*R2-C2^2*C3^2*C4^2*R1 = 0

 (11)

eq9 := Rin = 1/9

Rin = 1/9

 (12)

`` 

> 



fsolve({eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {C1, C2, C3, C4, R1, R2, R3, R4, Rin}, {C1 = lw .. up, C2 = lw .. up, C3 = lw .. up, C4 = lw .. up, R1 = lw .. up, R2 = lw .. up, R3 = lw .. up, R4 = lw .. up, Rin = lw .. up})

fsolve({Rin = 1/9, C1*C2*C3*C4(C1*R2*R3*R4+C2*R1*R3*R4+C3*R1*R2*R4+C4*R1*R2*R3) = 84, C1*C2*C3*C4(C1*C2*R3*R4+C1*C3*R2*R4+C1*C4*R2*R3+C2*C3*R1*R4+C2*C4*R1*R3+C3*C4*R1*R2) = 126, C1*C2*C3*C4*(C1*C2*C3*R4+C1*C2*C4*R3+C1*C3*C4*R2+C2*C3*C4*R1) = 36, C1*C2*C3*C4*(C1*C2*C3*R4+C1*C2*C4*R3+C1*C3*C4*R2+C2*C3*C4*R1)-Rin*C1^2*C2*C3*C4*R2*R3*R4-C1*C2^2*C3*C4*R1*R3*R4*Rin-C1*C2*C3^2*C4*R1*R2*R4*Rin-C1*C2*C3*C4^2*R1*R2*R3*Rin-C1*C2*C3*R1*R2*R3*R4-C1*C2*C4*R1*R2*R3*R4-C1*C3*C4*R1*R2*R3*R4-C2*C3*C4*R1*R2*R3*R4 = 0, C1*C2*C3*C4*(C1*R2*R3*R4+C2*R1*R3*R4+C3*R1*R2*R4+C4*R1*R2*R3)-C1^2*C2^2*C3^2*C4*R4*Rin-C1^2*C2^2*C3*C4^2*R3*Rin-C1^2*C2*C3^2*C4^2*R2*Rin-C1*C2^2*C3^2*C4^2*R1*Rin-C1^2*C2^2*C3*R3*R4-C1^2*C2^2*C4*R3*R4-C1^2*C2*C3^2*R2*R4-C1^2*C2*C4^2*R2*R3-C1^2*C3^2*C4*R2*R4-C1^2*C3*C4^2*R2*R3-C1*C2^2*C3^2*R1*R4-C1*C2^2*C4^2*R1*R3-C1*C3^2*C4^2*R1*R2-C2^2*C3^2*C4*R1*R4-C2^2*C3*C4^2*R1*R3-C2*C3^2*C4^2*R1*R2 = 0, C1*C2*C3*C4*(C1*C2*R3*R4+C1*C3*R2*R4+C1*C4*R2*R3+C2*C3*R1*R4+C2*C4*R1*R3+C3*C4*R1*R2)-C1^2*C2^2*C3*C4*R3*R4*Rin-C1^2*C2*C3^2*C4*R2*R4*Rin-C1^2*C2*C3*C4^2*R2*R3*Rin-C1*C2^2*C3^2*C4*R1*R4*Rin-C1*C2^2*C3*C4^2*R1*R3*Rin-C1*C2*C3^2*C4^2*R1*R2*Rin-C1^2*C2*C3*R2*R3*R4-C1^2*C2*C4*R2*R3*R4-C1^2*C3*C4*R2*R3*R4-C1*C2^2*C3*R1*R3*R4-C1*C2^2*C4*R1*R3*R4-C1*C2*C3^2*R1*R2*R4-C1*C2*C4^2*R1*R2*R3-C1*C3^2*C4*R1*R2*R4-C1*C3*C4^2*R1*R2*R3-C2^2*C3*C4*R1*R3*R4-C2*C3^2*C4*R1*R2*R4-C2*C3*C4^2*R1*R2*R3 = 0, -C1*C2*C3*C4*R1*R2*R3*R4*Rin+C1^2*C2^2*C3^2*C4^2 = 0, -C1^2*C2^2*C3^2*C4^2*Rin+C1*C2*C3*C4*R1*R2*R3*R4-C1^2*C2^2*C3^2*R4-C1^2*C2^2*C4^2*R3-C1^2*C3^2*C4^2*R2-C2^2*C3^2*C4^2*R1 = 0}, {C1, C2, C3, C4, R1, R2, R3, R4, Rin}, {C1 = 0.1e-1 .. 10, C2 = 0.1e-1 .. 10, C3 = 0.1e-1 .. 10, C4 = 0.1e-1 .. 10, R1 = 0.1e-1 .. 10, R2 = 0.1e-1 .. 10, R3 = 0.1e-1 .. 10, R4 = 0.1e-1 .. 10, Rin = 0.1e-1 .. 10})

 (13)
> 

``
> 

Ra := Rin*km

0.1784124116e-1*Rin/(6.8*e-9)

 (14)

 

NULL

> 

Cb := C1*km/kf

0.5679043442e-5*C1/(6.8*e-9)

 (15)
> 

 

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#im tryin to solve 9 equation having 9 varibales but the fsolve doesnt solve for C1 to R4, what i am doing wrong??
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