First Order Equations

Solutions ToWeb Site Examples

Here are some Maple solutions to web site Exam I examples 11-14, 16.

>	with(plots):

Example 11

>	ode11:=diff(y(x),x)=y(x)+x*y(x)^2;

>	dsolve(ode11,{y(x)});

>	dsolve({ode11,y(0)=-2},{y(x)});

>	f:=rhs(%);

>	soln1:=plot(f,x=-5..5,y=-10..10,color=red):

>	dsolve({ode11,y(0)=2},{y(x)});

>	g:=rhs(%);

>	soln2:=plot(g,x=-5..5,y=-10..10,color=blue):

>	display(soln1,soln2);

Example 12

>	ode12:=diff(y(x),x)=2*x*y(x)+(1/x)*y(x)*ln(y(x));

>	dsolve(ode12,{y(x)});

>	dsolve({ode12,y(1)=1},{y(x)});

>	f:=rhs(%);

>	soln3:=plot(f,x=1..2.2,y=0..40,color=red):

>	dsolve({ode12,y(1)=5},{y(x)});

>	g:=rhs(%);

>	soln4:=plot(g,x=1..2.2,y=0..40,color=blue):

>	display(soln3,soln4);

Example 13

>	ode3:=diff(y(x),x)=(1-x-y(x))/(x+y(x));

>	dsolve(ode3,{y(x)});

>	dsolve({ode3,y(0)=10},{y(x)});

>	f:=rhs(%);

>	plot(f,x=0..50,y=-50..20);

>	dsolve({ode3,y(0)=-10},{y(x)});

>	g:=rhs(%);

>	plot(g,x=0..50,y=-70..10);

Example 14

>

>	ode14:=diff(y(x),x)=y(x)/(x+x*ln(y(x))-x*ln(x));

>	dsolve(ode14,{y(x)});

>	dsolve({ode14,y(1)=exp(1)},{y(x)});

>	f:=rhs(%);

>	plot(f,x=1..21,y=0..20);

Example 16

>	ode16:=diff(s(t),t)=9-3*s(t)/50;

>	dsolve(ode16,{s(t)});

>	dsolve({ode16,s(0)=100},{s(t)});

>	dsolve({ode16,s(0)=10},{s(t)});

>	f:=rhs(%);

>	p1:=plot(f,t=0..100,color=red,labels=[t,s]):

>	p2:=plot(150,t=0..100,color=blue,labels=[t,s]):

>	display(p1,p2);

>