# NAME    :- IBRAR    
TUTORIAL:- GROUP 5TH
ROLL NO :- 11232225 
DATE    :- 15-1-2013

PLOT THE FAMILY OF SOLUTION OF FIRST ORDER
DIFFERENTIAL EQUATION

kill(all)$
depends(y,x);
eq:diff(y,x)=x^2;
sol:ode2(eq,y,x);
solx:ic1(sol,x=0,y=c);
gr1:ev(solx,c=0);
gr2:ev(solx,c=1);
gr3:ev(solx,c=2);
gr4:ev(solx,c=3);
wxplot2d([rhs(gr1),rhs(gr2),
rhs(gr3),rhs(gr4)],[x,-2,2]);

PLOT THE FAMILY OF SOLUTION OF SECOND ORDER 
DIFFERENTIAL EQUQTION
y"+3*y'+2*y=0 WITH y'(0)=b,
y(0)=1 b varies from -3 TO 3

kill(all)$
depends(y,x);
eq:diff(y,x,2)+3*diff(y,x)+2*y=0;
sol:ode2(eq,y,x);
solx:ic2(sol,x=0,y=1,diff(y,x)=b);
gr1:ev(solx,b=-3);
gr2:ev(solx,b=-2);
gr3:ev(solx,b=-1);
gr4:ev(solx,b=0);
gr5:ev(solx,b=1);
gr6:ev(solx,b=2);
gr7:ev(solx,b=3);
wxplot2d([rhs(gr1),rhs(gr2),
rhs(gr3),rhs(gr4),rhs(gr5),
rhs(gr6),rhs(gr7)],[x,-1,5],[y,-3,3]);

kill(all)$
depends(y,x);
eq:diff(y,x,2)+3*diff(y,x)+2*y=0;
sol:ode2(eq,y,x);
solx:ic2(sol,x=0,y=a,diff(y,x)=1);
gr1:ev(solx,a=-6);
gr2:ev(solx,a=-4);
gr3:ev(solx,a=-2);
gr4:ev(solx,a=0);
gr5:ev(solx,a=2);
gr6:ev(solx,a=4);
gr7:ev(solx,a=6);
wxplot2d([rhs(gr1),rhs(gr2),
rhs(gr3),rhs(gr4),rhs(gr5),
rhs(gr6),rhs(gr7)],[x,-1,5],[y,-6,6],
[legend,"y1","y2","y3","y4","y5","y5","y6","y7"]);