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I have the following problem I want to solve the following equalities.

My used code:

Clear["Global`*"] d = 0.75; qa[ta_] = (ta)^(1/ya) - 1; qb[tb_] = (tb)^(1/yb) - 1; ya = 3; yb = 2; SOLCEQ1 = Table[Solve[ qa'[ta]/Log[d] (d^(tb + 1)/d^(ta) - 1) == qa[ta] && qb'[tb]/Log[d] + qb[tb] == b qa[ta] && tb > ta && ta > 0, {tb, ta}], {b, 0.8, 1, 0.1}]

The answer is:

{{{tb -> 4.45415, ta -> 2.50827}}, {{tb -> 4.57749, ta -> 2.53496}}, {{tb -> 4.70672, ta -> 2.56222}}}

But if I now change (swap) ya and yb.

Code:

Clear["Global`*"] d = 0.75; qa[ta_] = (ta)^(1/ya) - 1; qb[tb_] = (tb)^(1/yb) - 1; ya = 2; yb = 3; SOLCEQ1 = Table[Solve[ qa'[ta]/Log[d] (d^(tb + 1)/d^(ta) - 1) == qa[ta] && qb'[tb]/Log[d] + qb[tb] == b qa[ta] && tb > ta && ta > 0, {tb, ta}], {b, 0.8, 1, 0.1}]

The answer is:

{Solve[-((1.73803 (-1 + 0.75^(1 - ta + tb)))/Sqrt[ta]) == -1 + Sqrt[ ta] && -1 - 1.15869/tb^(2/3) + tb^(1/3) == 0.8 (-1 + Sqrt[ta]) && tb > ta && ta > 0, {tb, ta}], Solve[-((1.73803 (-1 + 0.75^(1 - ta + tb)))/Sqrt[ta]) == -1 + Sqrt[ ta] && -1 - 1.15869/tb^(2/3) + tb^(1/3) == 0.9 (-1 + Sqrt[ta]) && tb > ta && ta > 0, {tb, ta}], Solve[-((1.73803 (-1 + 0.75^(1 - ta + tb)))/Sqrt[ta]) == -1 + Sqrt[ ta] && -1 - 1.15869/tb^(2/3) + tb^(1/3) == 1. (-1 + Sqrt[ta]) && tb > ta && ta > 0, {tb, ta}]}

So the programm do not start the Solve function process. I tried everything. If somebody knows a solution, I would be very thankful.

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Your claim "the programm [program] do [does] not start the Solve function process" is not true: the returned inputs mean the Solve cannot solve those and the message is performs. Making use of NMinimize instead of Solve, the following works in 13.3.1 on Windows 10:

Clear["Global`*"];d = 0.75;qa[ta_] = (ta)^(1/ya) - 1; qb[tb_] = (tb)^(1/yb) - 1;ya = 2;yb = 3; SOLCEQ1 = Table[NMinimize[{(qa'[ta]/Log[d] (d^(tb + 1)/d^(ta) - 1) - qa[ta])^2 + (qb'[tb]/Log[d] + qb[tb] - b qa[ta])^2, tb > ta && ta > 0}, {tb, ta}], {b, 0.8, 1, 0.1}]

{{5.44948*10^-21, {tb -> 7.05961, ta -> 3.07779}}, {1.38056*10^-20, {tb -> 7.99239, ta -> 3.19818}}, {7.22472*10^-22, {tb -> 9.06827, ta -> 3.30832}}}

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  • $\begingroup$ Thanks a lot for your answer. $\endgroup$ Commented Nov 14, 2023 at 15:01

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