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I have two fourth order differential equations and eight boundary conditions. I want to get my result in terms of function (Y) and coefficients (let say P1, P2 and so on). I used Dsolve to get the solution and simplified the result but still, the result is too long. How can I further transform it in to simplify form? Any help will be appreciated.

eq1 = X''''[Y] - 
A6*X''[Y] - (-Bi D5 + (A0^2 - Bi) D1 Cosh[
     A0 Y] + (4 A0^2 - Bi) D3 Cosh[2 A0 Y] + A0^2 D2 Sinh[A0 Y] - 
   Bi D2 Sinh[A0 Y] + 4 A0^2 D4 Sinh[2 A0 Y] - 
   Bi D4 Sinh[2 A0 Y])/k == 0;
eq2 = Z''''[Y] - 
A6*Z''[Y] + (Bi (D5 + D1 Cosh[A0 Y] + D3 Cosh[2 A0 Y] + 
     D2 Sinh[A0 Y] + D4 Sinh[2 A0 Y]))/k == 0;

Simplify[DSolveValue[{eq1, eq2, Z[0]== 0, X''[t]==B3, Z''[t]== 0, X[t] == Z[t],B2 == -k*X'[t] - Z'[t]}, {X[Y], Z[Y]}, Y]] 

Note: A0,A6,B2,B3,B4,D1 to D5,Bi,k are constant values.

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  • $\begingroup$ Do you have any reason to expect that further simplifications are in fact possible? $\endgroup$ – AccidentalFourierTransform May 31 at 13:17
  • $\begingroup$ What if any constraints exist on the constants? Are any real, or nonnegative, or positive, or negative, or restricted to an interval? Adding corresponding assumptions to Simplify might help. $\endgroup$ – Bob Hanlon May 31 at 17:14
  • $\begingroup$ All the constants are real and positive and not restricted to an interval @BobHanlon $\endgroup$ – MIRZA FARRUKH BAIG Jun 1 at 8:37
  • $\begingroup$ Actually, I want to simplify my answer and I think in Mathematica there should be a way to simplify the result in a manner. @AccidentalFourierTransform $\endgroup$ – MIRZA FARRUKH BAIG Jun 1 at 9:42
  • $\begingroup$ Then you should use Assuming[Thread[{A0, A6, B2, B3, Bi, D1, D2, D3, D4, D5, k} > 0], Simplify[ DSolveValue[ {eq1, eq2, Z[0] == 0, X''[t] == B3, Z''[t] == 0, X[t] == Z[t], B2 == -k*X'[t] - Z'[t]}, {X[Y], Z[Y]}, Y]]]. Although in this case the result does not simplify further, you should not withhold information from Mathematica. You might also try using FullSimplify but it will take an inordinate amount of time and there is no guarantee that further simplification is possible. $\endgroup$ – Bob Hanlon Jun 1 at 15:20

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