MATLAB: Symbolic integration using ‘int’: Find integration constant using symbolic initial condition

integration constantMATLABsymbolic integgration

Hi, using 'syms' and 'int' I solve symbolic integral, which provides me the answer with integration constant 'C'. The result is a long-expression and I wish to define the initial condition, e.g., y(0)=a, so I can find the closed-form expression with the integration constant.

Is there a way to define symbolic initial conditions and get the complete solution?

best,

Best Answer

constant = a - subs(TheExpression,Variable,0) + C

For example, TheExpression(0) might be 5+C and a might be 2, and 2 - (5+C) + C = 2-5 = -3 which is the constant of integration

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MATLAB: Symbolic Integration

Both answers are correct.

d/dx[ (x+y)^2/2 ] = d/dx[ x^2/2 + x*y + y^2/2 ] = x + y

d/dx[ x^2/2 + x*y ] = x + y

The ambiguity lies in the constant of integration. In the first case the constant of integration ends up being y^2/2.

If you really want to enforce that the constant of integration is zero then do:

F = int(x+y,x,0,x)
expand(F)

MATLAB: Symbolic Integration Bug

No bug. You are doing indefinite integration, which is permitted to have a constant of integration. You are evaluating at a single point rather than evaluating the difference between two locations, so the constant of integration is included in the value. It is permitted for the two forms to generate two different constants of integration.

If you were to

syms a
Maint = int(Ma, x, a, x);
Mbint = int(Mb, x, a, x);

then you would get the same result for the two.

Best Answer

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