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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart;\nwith(plots
):\nwith(DEtools):" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 65 "Example 1:
 An Electric Circuit with constant voltage (DC voltage)" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 19 "Clear the variable " }{XPPEDIT 18 0 "y;" 
"6#%\"yG" }{TEXT -1 45 ", which currently is defined as a function.\n \+
" }{MPLTEXT 1 0 7 "y:='y':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "A d
ifferential equation for an electric circuit" }{MPLTEXT 1 0 32 "\nDE2:
=12*y(x)+4*diff(y(x),x)=60;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "A \+
particular solution plotted on the slope field" }{MPLTEXT 1 0 171 "\ni
nitialCondition:=[[0,0]];\nDEplot(DE2, y(x), x=-1..7,initialCondition,
y=-1..7,linecolor=blue,title=\"Particular solution to an electric circ
uit diff. eq. through (0,0)\");\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
51 "Several particular solutions plotted simultaneously" }{MPLTEXT 1 
0 167 "\nmoreInitConds:=[[0,0],[0,5],[0,7]];\nDEplot(DE2, y(x), x=-1..
7,moreInitConds,y=-1..7,linecolor=[blue,red,maroon],title=\"Several pa
rticular solutions to y'(x)=15-3*y\");" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 256 16 "General solution" }{TEXT -1 46 " to the electric circuit
 differential equation" }{MPLTEXT 1 0 19 "\ndsolve(DE2, y(x));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Clear the value of C1, which was p
reviously used.\n" }{MPLTEXT 1 0 9 "C1:='C1':" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 56 "subs(\{y(x)=0,x=0\},y(x)=5+exp(-3*x)*C1);\nC1:=s
olve(%,C1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 19 "Particular soluti
on" }{TEXT -1 28 " for initial condition (0,0)" }{MPLTEXT 1 0 107 "\ny
:=x->5+exp(-3*x)*C1;\nplot(y(x),x=-1..7,y=-1..7,title=\"Particular sol
ution to y'(x)=15-3y through (0,0)\");" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 68 "Example 2: An Electric Circuit with oscil
lating voltage (AC voltage)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Cle
ar the variable " }{XPPEDIT 18 0 "y;" "6#%\"yG" }{TEXT -1 43 ", which \+
currently is defined as a function." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
36 "restart;\nwith(plots):\nwith(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 47 "A differential equation for an electric circuit" }
{MPLTEXT 1 0 69 "\ny:='y':  #Clear value of y\nDE3:=12*y(x)+4*diff(y(x
),x)=60*sin(60*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "dsolv
e(\{DE3,y(0)=0\},y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "
assign(%);\ny:=unapply(y(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 127 "plot1:=plot(y(x),x=0..1,y=-1..1,color=red,legend=\"Current\")
:\ndisplay(plot1,title=\"Circuit under alternating voltage (~9.5Hz)\")
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 147 "plot2:=plot(sin(60*x)
/3,x=0..1,y=-1..1,color=blue,legend=\"Voltage / 180\"):\ndisplay([plot
1,plot2],title=\"Current and voltage/180 plotted together\");" }}}
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