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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "# Quadrature problem
; several solution curves\n\n# filename = 01.3.mws\n\nrestart;\n\nint(
3*x^2-4*x,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "cvals:=seq
(2*i,i=-5..5):\ntoplot:=[seq(x^3-2*x^2+c,c=cvals)]:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "nops(toplot);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 42 "plot(toplot,x=-2..3,view=[-2..3,-15..15]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot(x^3-2*x^2+5,x=-2..3,vie
w=[-2..3,-15..15]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Example 1:
 dsolve with and without initial conditions" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 42 "gensol:=dsolve(diff(v(t),t)=32-v(t),v(t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "gensol:=dsolve(\{diff(v(t),t
)=32-v(t),v(0)=0\},v(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Exam
ple 2: dsolve with and without initial conditions" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 54 "exactsol:=dsolve(\{diff(y(x),x)=sin(x^2),y(0
)=0\},y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "?FresnelS" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "numsol:=dsolve(\{diff(y(x)
,x)=sin(x^2),y(0)=0\},y(x),numeric);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "odeplot(numsol,[x,y(x)],0..10);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "numsol(5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Ex
ample 3: dsolve with and without initial conditions" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 40 "sol:=dsolve(diff(x(t),t$2)+x(t)=0,x(t));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "dsolve(\{diff(x(t),t$2)
+x(t)=0,x(0)=0,D(x)(0)=1\},x(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
41 "Example 4: 2-point boundary value problem" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 42 "dsolve(diff(y(x),x$2)+Pi^2/4*y(x)=0,y(x));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "dsolve(\{diff(y(x),x$2)+Pi^2
/4*y(x)=0,y(0)=0,y(1)=2\},y(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "plot(2*sin(1/2*Pi*x),x=0..1);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "?DEtools" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "with(DEtools);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "
DEplot(diff(x(t),t$2)+(1/3*diff(x(t),t)^2-1)*diff(x(t),t)+x(t)=0,x(t),
t=0..15,[[x(0)=1,D(x)(0)=0]],stepsize=0.1,linecolor=BLACK);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "DEplot(diff(x(t),t$2)+(1/3*
diff(x(t),t)^2-1)*diff(x(t),t)+x(t)=0,x(t),t=0..15,[[x(0)=0.1,D(x)(0)=
0],[x(0)=0,D(x)(0)=1.9]],stepsize=0.1,linecolor=[BLACK,GRAY]);" }}}
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