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Question: How do i solve this laplace problem???

Question:How do i solve this laplace problem???

pedromneto 5 Maple 17
laplace-transform
June 28 2014
1

What´s the error here??????

Solução do Sistema de EDO's por Transformada de Laplace
 
> 

restart
> 

with(inttrans):
> 

eq1 := diff(x(t), t)+(2.2*x(t)*y(t)+0.5e-1*x(t)/(5+0.5e-1*t)) = 0;

diff(x(t), t)+2.2*x(t)*y(t)+0.5e-1*x(t)/(5+0.5e-1*t) = 0

 (1)
> 

eq2 := diff(y(t), t)+(2.2*x(t)*y(t)-(0.5e-1*(0.25e-1-y(t)))/(5+0.5e-1*t)) = 0;

diff(y(t), t)+2.2*x(t)*y(t)-0.5e-1*(0.25e-1-y(t))/(5+0.5e-1*t) = 0

 (2)
> 

eq3 := diff(z(t), t)-2.2*x(t)*y(t)+0.5e-1*z(t)/(5+0.5e-1*t) = 0;

diff(z(t), t)-2.2*x(t)*y(t)+0.5e-1*z(t)/(5+0.5e-1*t) = 0

 (3)
> 

EQ := [eq1, eq2, eq3]:
> 

for i to 3 do La[i] := laplace(EQ[i], t, s) end do;

s*laplace(x(t), t, s)-1.*x(0.)+2.200000000*laplace(x(t)*y(t), t, s)+laplace(x(t)/(100.+t)^1., t, s) = 0.

  

-1.*y(0.)-0.2500000000e-1*(exp(100.*s))^1.*Ei(1., 100.*s)^1.+1.*s^1.*laplace(y(t), t, s)^1.+2.200000000*laplace(x(t)^1.*y(t)^1., t, s)+1.*laplace(y(t)^1./(100.+1.*t)^1., t, s) = 0.

  

s*laplace(z(t), t, s)-1.*z(0.)-2.200000000*laplace(x(t)*y(t), t, s)+laplace(z(t)/(100.+t)^1., t, s) = 0.

 (4)
> 

LL := subs({laplace(x(t), t, s) = X, laplace(y(t), t, s) = Y, laplace(z(t), t, s) = Z}, [La[1], La[2], La[3]]);

[s*X-1.*x(0.)+2.200000000*laplace(x(t)*y(t), t, s)+laplace(x(t)/(100.+t)^1., t, s) = 0., -1.*y(0.)-0.2500000000e-1*(exp(100.*s))^1.*Ei(1., 100.*s)^1.+1.*s^1.*Y^1.+2.200000000*laplace(x(t)*y(t), t, s)+1.*laplace(y(t)/(100.+t)^1., t, s) = 0., s*Z-1.*z(0.)-2.200000000*laplace(x(t)*y(t), t, s)+laplace(z(t)/(100.+t)^1., t, s) = 0.]

 (5)
> 

sol := solve(LL, [X, Y, Z]):
> 

assign(sol):
> 

SOLS[X, Y, Z]:
> 

SOLT := map(invlaplace, [X, Y, Z], s, t);

[-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(x(_U1)/(100.+_U1), _U1 = 0. .. t))+x(0), -1.*(int(y(_U1)/(100.+_U1), _U1 = 0. .. t))-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))+y(0)+0.2500000000e-1*ln(1.+0.1000000000e-1*t), 2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(z(_U1)/(100.+_U1), _U1 = 0. .. t))+z(0)]

 (6)
> 

SOLTT := evalf(subs({x(0) = 0.5e-1, y(0) = 0, z(0) = 0}, SOLT));

[-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(x(_U1)/(100.+_U1), _U1 = 0. .. t))+0.5e-1, -1.*(int(y(_U1)/(100.+_U1), _U1 = 0. .. t))-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))+0.2500000000e-1*ln(1.+0.1000000000e-1*t), 2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(z(_U1)/(100.+_U1), _U1 = 0. .. t))]

 (7)
> 

xx := evalc(Re(SOLTT[1]));

-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(x(_U1)/(100.+_U1), _U1 = 0. .. t))+0.5e-1

 (8)
> 

yy := evalc(Re(SOLTT[2]));

0.2500000000e-1*ln(abs(1.+0.1000000000e-1*t))-1.*(int(y(_U1)/(100.+_U1), _U1 = 0. .. t))-2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))

 (9)
> 

zz := evalc(Re(SOLTT[3]));

2.200000000*(int(x(_U1)*y(_U1), _U1 = 0. .. t))-1.*(int(z(_U1)/(100.+_U1), _U1 = 0. .. t))

 (10)
> 

plot([xx, yy, zz], t = 0 .. 500, legend = [x, y, z]);

Warning, expecting only range variable t in expression -2.200000000*int(x(_U1)*y(_U1),_U1 = 0. .. t)-1.*int(x(_U1)/(100.+_U1),_U1 = 0. .. t)+.5e-1 to be plotted but found names [_U1, x, y]

  

 

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