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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Solve ordinary differentia
l equation: (initial value problem)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "eq:=diff(u(x),x,x)+2*u(x)=0; dsolve(\{eq\},\{u(x)\});
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "ini:= u(0)=5, D(u)(0)=1
; dsolve(\{eq,ini\},\{u(x)\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 43 "sol:=dsolve(\{eq,ini\},\{u(x)\}, type=numeric);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "sol(1); sol(2);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 27 "odeplot(sol,[x,u(x)],0..5);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 33 "How about boundary value problem?" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "eq1:=diff(u(x),x,x)+2*u(x)=0; gener
al_solution:=dsolve(\{eq1\},u(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "dsolve(\{eq1,u(0)=2,u(1)=3\},\{u(x)\});" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "u1:=rhs(%);" }}}{EXCHG }{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(u1,x=0..5);" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 44 "Now let's solve some PDE: diffusion equation" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "with(PDEtools): diffusion:=diff(u(
t,x),t)=2*diff(u(t,x),x,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
43 "pdsolve(diffusion, u(t,x), HINT=X(x)*T(t));" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 52 "pdsolve(diffusion, u(t,x), HINT=X(x)*T(t), 'bu
ild');" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT -1 31 "Here is \+
the numerical solution:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "IBC:=\{u
(0,x)=sin(Pi*x), u(t,0)=0, u(t,1)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "pds:=pdsolve(diffusion, IBC, numeric, spacestep=1/40)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "pds:-animate(t=0.2,fra
mes=100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
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