Math260-023 (A. Farhat)
         Maple Project Solution

Use the restart command to start the kernel

> restart;

Load 'DEtools' and 'linalg' packages

> with(DEtools):

> with(linalg):

Define the differential equation and name it de

> de:=diff(y(x),x$5)-3*diff(y(x),x$4)-12*diff(y(x),x$3)+42*diff(y(x),x$2)+32*diff(y(x),x)-120*y(x)=0;

de := diff(y(x),`$`(x,5))-3*diff(y(x),`$`(x,4))-12*...

Use the 'dsolve' commnad to solve the diff. eqn.

> dsolve(de,output=basis);

[exp(-2*x), exp(-3*x), exp(2*x), exp(3*x)*sin(x), e...

Use 'dsolve' command with the extra argument 'output=basis' to compute the basis of the solution space. Name the bais 'bas'

> bas:=dsolve(de,output=basis);

bas := [exp(-2*x), exp(-3*x), exp(2*x), exp(3*x)*si...

Use the 'Wronskian' command to compute the wronskian matrix of the basis (bas.) Name it w.

> w:=Wronskian(bas,x);

w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...
w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...
w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...
w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...
w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...
w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...
w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...
w := matrix([[exp(-2*x), exp(-3*x), exp(2*x), exp(3...

Use the 'det' command to compute the wronskian (w) of the basis

> det(w);

38480*exp(-2*x)*exp(-3*x)*exp(2*x)*exp(3*x)^2*sin(x...

Use the 'simplify' command to simplify computed wronskian;

> simplify(%);

38480*exp(3*x)

Use the 'dsolve' command to find a particular solution satisfying the initial conditions

> dsolve({de,y(0)=962,D(y)(0)=0,(D@@2)(y)(0)=0,(D@@3)(y)(0)=0,(D@@4)(y)(0)=0},y(x));

y(x) = 555*exp(-2*x)-208*exp(-3*x)+1443*exp(2*x)+84...

Use the 'odeadvisor' command to classify the diff. eqn.

> odeadvisor(de);

Compare your answers to the answers you obtained using Mathcad

>

> de1:=diff(x1(t),t)=2*x1(t);

>

de1 := diff(x1(t),t) = 2*x1(t)

> de2:=diff(x2(t),t)=-7*x1(t)+9*x2(t)+7*x3(t);

de2 := diff(x2(t),t) = -7*x1(t)+9*x2(t)+7*x3(t)

> de3:=diff(x3(t),t)=2*x3(t);

de3 := diff(x3(t),t) = 2*x3(t)

> dsolve({de1,de2,de3},{x1(t),x2(t),x3(t)});

{x3(t) = _C2*exp(2*t), x1(t) = _C3*exp(2*t), x2(t) ...

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> de1:=diff(x1(t),t)=-2*x1(t)+17*x2(t)+4*x3(t);

de1 := diff(x1(t),t) = -2*x1(t)+17*x2(t)+4*x3(t)

> de2:=diff(x2(t),t)=-x1(t)+6*x2(t)+1*x3(t);

de2 := diff(x2(t),t) = -x1(t)+6*x2(t)+x3(t)

> de3:=diff(x3(t),t)=x2(t)+2*x3(t);

de3 := diff(x3(t),t) = x2(t)+2*x3(t)

> dsolve({de1,de2,de3},{x1(t),x2(t),x3(t)});

{x3(t) = 1/2*(2*_C2*t+_C3*t^2+2*_C1)*exp(2*t), x1(t...
{x3(t) = 1/2*(2*_C2*t+_C3*t^2+2*_C1)*exp(2*t), x1(t...

> dsolve({de1,de2,de3,x1(0)=1,x2(0)=-1,x3(0)=0},{x1(t),x2(t),x3(t)});

{x3(t) = 1/2*(-2*t-5*t^2)*exp(2*t), x1(t) = 1/2*exp...

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