Solve a function in terms of a variable?

Question

Matthew Holub 2015-4-13

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https://ww2.mathworks.cn/matlabcentral/answers/197861-solve-a-function-in-terms-of-a-variable

编辑： Roger Stafford 2015-4-13

I need to find this equation in terms of M2:

syms M M1 M2 Alpha
dAlpha = sqrt((M^2)-1)/(M*(1+(.2*(M^2))));
integralAlpha = int(dAlpha,M)
eqn = subs(integralAlpha,M,M2) - subs(integralAlpha,M,M1) == Alpha
sol = solve(eqn,M2)

but I am getting an error that says:

Warning: Cannot find explicit solution. 
> In solve at 319
  In Testing at 8 
sol =
Empty sym: 0-by-1

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Answer 1

Roger Stafford 2015-4-13

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https://ww2.mathworks.cn/matlabcentral/answers/197861-solve-a-function-in-terms-of-a-variable#answer_174954

编辑：Roger Stafford 2015-4-13

在 MATLAB Online 中打开

If my memory serves me correctly, that function will give rise to elliptic integrals of the first and second kinds, incomplete. That may be why 'solve' failed to come up with an explicit solution. However, before you give up on 'solve' I would suggest you place the limits, M1 and M2, as arguments in 'int' itself instead of first getting an indefinite integral:

integralAlpha = int(dAlpha,M,M1,M2);

If that fails, then try using numerical integration with specific values for M1 and M2, and use 'fzero' instead of 'solve'.