First Order Equations

Solutions ToWeb Site Examples

Here is some Maple code to solve  web site Exam I example 10 and graph the solution.

Example 10

First solve for x between 0 and 3.

>	ode1:=diff(y(x),x)=-2*y(x)+1;

>	dsolve(ode1,{y(x)});

>	dsolve({ode1,y(0)=0},{y(x)});

>	f:=rhs(%);

Now solve for x greater than 3 with the necessary value for y(3) to give continuity at x = 3.

>	ode2:=diff(y(x),x)=-2*y(x);

>	dsolve({ode2,y(3)=1/2-exp(-6)/2},{y(x)});

>	g:=rhs(%);

Graph the solution.

>	h:=x->piecewise(x<=3,f,g);

>	with(plots):

Warning, the name changecoords has been redefined

>	plot(h(x),x=0..6,y=0..0.6);

Here is another way of defining the solution function.

>	q(x):=piecewise(x<=3,f,g);

>	plot(q(x),x=0..6,y=0..0.6);

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