Question: Four equations in four unknowns

 

phi := sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh(Pi/(4*y))+c__4*y*sinh((1/4)*Pi*y));

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(1)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(2)

diff((2), y);

sin((1/4)*Pi*x)*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

(3)

diff((3), y);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c__3*cosh((1/4)*Pi/y)*Pi^2/y^3+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2)

(4)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(5)

diff((5), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(6)

diff((6), x);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(7)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(8)

diff((8), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(9)

diff((9), y);

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

(10)

``

(11)

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))=0;

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y)) = 0

(12)

eval( (12), [x = 0]);

0 = 0

(13)

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y)) = 0

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y)) = 0

(14)

eval( (14), [x = 20]);

0 = 0

(15)

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = 0

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = 0

(16)

eval( (16), [y = 9]);

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((9/4)*Pi)+(1/11664)*c__3*Pi^2*cosh((1/36)*Pi)+(1/2)*c__4*Pi*cosh((9/4)*Pi)+(9/16)*c__4*Pi^2*sinh((9/4)*Pi)) = 0

(17)

evalf[5]( (17) );

sin(.78540*x)*(362.25*c__1+0.84938e-3*c__3+4182.6*c__4) = 0.

(18)

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = -sin((1/4)*pi*x);

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = -sin((1/4)*pi*x)

(19)

eval( (19), [y = -9]);

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((9/4)*Pi)-(1/11664)*c__3*Pi^2*cosh((1/36)*Pi)+(1/2)*c__4*Pi*cosh((9/4)*Pi)+(9/16)*c__4*Pi^2*sinh((9/4)*Pi)) = -sin((1/4)*pi*x)

(20)

evalf[5]( (20) );

sin(.78540*x)*(362.25*c__1-0.84938e-3*c__3+4182.6*c__4) = -1.*sin(.25000*pi*x)

(21)

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

(22)

eval( (22), [y = 9]);

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((9/4)*Pi)*Pi+c__3*cosh((1/36)*Pi)-(1/36)*c__3*sinh((1/36)*Pi)*Pi+c__4*sinh((9/4)*Pi)+(9/4)*c__4*Pi*cosh((9/4)*Pi)) = 0

(23)

evalf[5]( (23) );

-.78540*cos(.78540*x)*(461.22*c__1+.99617*c__3+4738.2*c__4) = 0.

(24)

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0;

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

(25)

eval( (25), [y = -9]);

-(1/4)*cos((1/4)*Pi*x)*Pi*(-(1/4)*c__1*sinh((9/4)*Pi)*Pi+c__3*cosh((1/36)*Pi)-(1/36)*c__3*sinh((1/36)*Pi)*Pi-c__4*sinh((9/4)*Pi)-(9/4)*c__4*Pi*cosh((9/4)*Pi)) = 0

(26)

evalf[5]( (26) );

-.78540*cos(.78540*x)*(-461.22*c__1+.99617*c__3-4738.2*c__4) = 0.

(27)

s:=solve({sin(.78540*x)*(362.25*c__1+0.84938e-3*c__3+4182.6*c__4) = 0,sin(.78540*x)*(362.25*c__1-0.84938e-3*c__3+4182.6*c__4) = -1.*sin(.25000*Pi*x),-.78540*cos(.78540*x)*(461.22*c__1+.99617*c__3+4738.2*c__4) = 0,-.78540*cos(.78540*x)*(-461.22*c__1+.99617*c__3-4738.2*c__4) = 0},{c1,c2,c3,c4});

{c__1 = 0., c__3 = 0., c__4 = 0., x = 0.}, {c__1 = -10.27318850*c__4, c__3 = 0., c__4 = c__4, x = 0.}, {c__1 = -11.54616977*c__4-0.1380262250e-2, c__3 = 588.6646731, c__4 = c__4, x = -1.999995323}, {c__1 = -11.54616977*c__4-0.1380262250e-2, c__3 = 588.6646731, c__4 = c__4, x = 1.999995323}

(28)

``

 

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