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;

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

> dsolve(de,output=basis);

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);

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

> w:=Wronskian(bas,x);

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

> det(w);

Use the 'simplify' command to simplify computed wronskian;

> simplify(%);

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));

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);

>

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

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

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

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> 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);

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

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

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

>