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Mathematics Calculus Equation Solving Wolfram Language

Loop of solving integrals constants doesn't work properly?

Nomsa Ledwaba

Posted 2 months ago

There are 6 steps whereby I use DSolve, then Update and evaluate the Mathematica package. Each step the output yields a function which contains obviously integration constants. For example Step 2 output yields a function with integration constants C1 , C2, C3 . Step 3 outputs yields a function with integration constants C1, C2 (instead of C4 , C5). Step 4 outputs a function with integration constants, C1, C2 (instead of C6 , C7). See attachment May you please assist with a way of achieving obtaining continuous integration constants.

POSTED BY: Nomsa Ledwaba

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 2 months ago

Yes, you can, if you like constants of the form `C$5267`. Another way: constantCounter = 1; DSolve[y''[x] == y[x], y, x, GeneratedParameters -> (C[constantCounter++] &)] DSolve[y''[x] == y[x], y, x, GeneratedParameters -> (C[constantCounter++] &)] although I don't understand the jumps in the numbers that come out.

POSTED BY: Gianluca Gorni

Nomsa Ledwaba

Posted 2 months ago

In my case is the partial derivative of u[x,t]. This is what I have written: constantCounter = 1; DSolve[ D[u[x, t], {x, 2}] == -(3 /(2k\[Theta])) x D[u[x, t], t] - k 3 /(2k\[Theta]) x (\[Theta] - x) D[u[x, t], x] + 3 /(2k\[Theta]) xx u[x, t] (y''[x]==y[x])(EDs[[5]]), u, x, t, GeneratedParameters -> (C[constantCounter++] &)] This is the Output: DSolve[ \!\(\SuperscriptBox[\(u\), TagBox[ RowBox[{"(", RowBox[{"2", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[x, t] == (3 x^2 u[x, t])/(2 k \[Theta]) - ( 3 x \!\(\SuperscriptBox[\(u\), TagBox[ RowBox[{"(", RowBox[{"0", ",", "1"}], ")"}], Derivative], MultilineFunction->None]\)[x, t])/(2 k \[Theta]) - ( 3 x (-x + \[Theta]) \!\(\*SuperscriptBox[\(u\), TagBox[ RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[x, t])/(2 \[Theta]), u, x, t, GeneratedParameters -> (C[constantCounter++] &)] No evaluation. Please advise how to enter partial differential equation for this GeneratedParameters command to work.

In my case is the partial derivative of u[x,t]. This is what I have written:

constantCounter = 1;
DSolve[ D[u[x, t], {x, 2}] == -(3 /(2*k*\[Theta])) x  D[u[x, t], t] - 
   k  3 /(2*k*\[Theta]) x  (\[Theta] - x) D[u[x, t], x] + 
   3 /(2*k*\[Theta])  x*x * 
    u[x, t] (*y''[x]==y[x]*)(*EDs[[5]]*), u, x, t, 
 GeneratedParameters -> (C[constantCounter++] &)]

This is the Output:

DSolve[
\!\(\*SuperscriptBox[\(u\), 
TagBox[
RowBox[{"(", 
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, t] == (3 x^2 u[x, t])/(2 k \[Theta]) - (
   3 x 
\!\(\*SuperscriptBox[\(u\), 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, t])/(2 k \[Theta]) - (
   3 x (-x + \[Theta]) 
\!\(\*SuperscriptBox[\(u\), 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, t])/(2 \[Theta]), u, x, t, 
 GeneratedParameters -> (C[constantCounter++] &)]

No evaluation. Please advise how to enter partial differential equation for this GeneratedParameters command to work.

POSTED BY: Nomsa Ledwaba

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 2 months ago

It is not a question of parameters, rather, the equation is just too difficult to solve: DSolve[D[u[x, t], {x, 2}] == -(3/(2k\[Theta])) x D[u[x, t], t] - k 3/(2k\[Theta]) x (\[Theta] - x) D[u[x, t], x] + 3/(2k\[Theta]) xxu[x, t] , u, {x, t}] Sorry, I realized now that my suggestion `GeneratedParameters -> (C[constantCounter++] &)` can give wrong formulas: constantCounter = 1; eq = D[u[x, t], {x, 2}] == D[u[x, t], t]; sol = DSolveValue[eq, u, {x, t}, GeneratedParameters -> (C[constantCounter++] &)] eq /. u -> sol /. {t -> 0, x -> 1, C[4 \| 5] -> 0, C[7 \| 8] -> 1, C[6] -> 0}

It is not a question of parameters, rather, the equation is just too difficult to solve:

DSolve[D[u[x, t], {x, 2}] == -(3/(2*k*\[Theta])) x D[u[x, t], t] - 
   k 3/(2*k*\[Theta]) x (\[Theta] - x) D[u[x, t], x] + 
   3/(2*k*\[Theta]) x*x*u[x, t] , u, {x, t}]

Sorry, I realized now that my suggestion GeneratedParameters -> (C[constantCounter++] &) can give wrong formulas:

constantCounter = 1;
eq = D[u[x, t], {x, 2}] == D[u[x, t], t];
sol = DSolveValue[eq,
  u, {x, t},
  GeneratedParameters -> (C[constantCounter++] &)]
eq /. u -> sol /.
 {t -> 0, x -> 1, C[4 | 5] -> 0, C[7 | 8] -> 1, C[6] -> 0}

POSTED BY: Gianluca Gorni

Nomsa Ledwaba

Posted 2 months ago

This is what I've written in place of the equation. I only replaced the differential equation. 'eq = D[u[x, t], {x, 2}] == -(3 /(2k\[Theta])) x D[u[x, t], t] - k 3 /(2k\[Theta]) x (\[Theta] - x) D[u[x, t], x] + 3 /(2k\[Theta]) xx u[x, t]; sol = DSolve(Value)[eq, u, {x, t}, GeneratedParameters -> (C[constantCounter++] &)] eq /. u -> sol /. {t -> 0, x -> 1, C[1 \| 2] -> 0, C[4 \| 5] -> 1, C[7 \| 8] -> 0, C[6] -> 1}' However, there are errors: DSolve::dsvar: 1 cannot be used as a variable. General::stop: Further output of DSolve::dsvar will be suppressed during this calculation. Increment::rvalue: constantCounter is not a variable with a value, so its value cannot be changed.