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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "White test.1.  (a) and (b)
 both  linear, constant coefficients,  not homogeneous." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "d2:=x^2*diff(y(x),x,x)-6*y(x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "simplify(subs(y(x)=x^3,d2));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "simplify(subs(y(x)=x^3*
v(x),d2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "subs(diff(v(x
),x)=u(x),%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dsolve(%,u
(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y2:=int(rhs(%),x)*
x^3;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "So the answer is " }
{XPPEDIT 18 0 "x^(-2);" "6#)%\"xG,$\"\"#!\"\"" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 2 "3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "de
t(wronskian([cosh(x),exp(x)],x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "solve(%=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 
"There are no solutions because " }{XPPEDIT 18 0 "sinh(x) < cosh(x);" 
"6#2-%%sinhG6#%\"xG-%%coshG6#F'" }{TEXT -1 9 " for all " }{XPPEDIT 18 
0 "x;" "6#%\"xG" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 75 "ivp4:=\{4*diff(y(x),x,x)+20*diff(y(x),x)+25*y(x)=sin(x), y(0)=
0, D(y)(0)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve(i
vp4,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "de5:=diff(y(x
),x,x)+y(x)=tan(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsol
ve(de5,y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "To do it by hand
, diff the first eq, sub y' from the second, solve the first for y, an
d sub that." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "e1:=diff(x(t
),t)=x(t)-y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "e2:=diff
(y(t),t)=-x(t)+2*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "e
1d:=diff(e1,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "d1ds:=su
bs(e2,e1d);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "se1y:=solve(
e1,y(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "sol6:=subs(y(t
)=se1y,d1ds);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Yellow test.   (
a)  is  linear, constant coefficients,  not homogeneous.  (b) is not l
inear." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart; with(lin
alg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "det(wronskian([exp
(x)*cos(x),exp(x)*sin(x)],x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "solve(%=0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "It is no
t zero because it is \n" }{XPPEDIT 18 0 "exp(2*x);" "6#-%$expG6#*&\"\"
#\"\"\"%\"xGF(" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 30 "d3:=x^2*diff(y(x),x,x)-2*y(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "simplify(subs(y(x)=x^2,d3));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 33 "simplify(subs(y(x)=x^2*v(x),d3));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "subs(diff(v(x),x)=u(x),%);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "dsolve(%,u(x));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y2:=int(rhs(%),x)*x^2;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 17 "So the answer is " }{XPPEDIT 18 0 "1/x;" 
"6#*&\"\"\"\"\"\"%\"xG!\"\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 
-1 2 "4." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "dsolve(\{diff(y
(x),x,x)+y(x)=tan(x),y(0)=0,D(y)(0)=0\},y(x));" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 2 "5." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "dsol
ve(4*diff(y(x),x,x)+20*diff(y(x),x)+25*y(x)=sin(x), y(x));" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 101 "6.  To do it by hand, diff the first eq,
 sub y' from the second, solve the first for y, and sub that." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "e1:=diff(x(t),t)=x(t)+y(t);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "e2:=diff(y(t),t)=-x(t)-
2*y(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "e1d:=diff(e1,t);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "d1ds:=subs(e2,e1d);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "se1y:=solve(e1,y(t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "sol6:=subs(y(t)=se1y,d1ds);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "I did both tests in 30 minute
s." }}}}{MARK "46" 0 }{VIEWOPTS 1 1 0 2 1 1805 }