# Question:Verifying whether two formulas are equal or not

## Question:Verifying whether two formulas are equal or not

Maple

Is the following function w

equal to next functions for a=1 or a= -1?

if a=1 then

w=

if a=-1 then

w=

where n>1, B,c and k are arbitrary constants.

################################
restart:
a:=-1:
B:=0:
c:=2:
h:=1:

#assume(n>1):
n:=3:
assume(0<=x and x<h):
assume(0<=t and t<h):

a:=-1:
if is(a>0)=true then
omega:=(x,t)->((2*c*n/(a*(n+1)))*(sin ((x-c*t+B)*sqrt(a)*(n-1)/(2*n)))^2 )^(1/(n-1));
print(omega(x,t));
elif is(a<0)=true then
omega:=(x,t)->(-(2*c*n/(a*(n+1)))*sinh ((x-c*t+B)*sqrt(-a)*(n-1)/(2*n))^2 )^(1/(n-1));
print(omega(x,t));
end if:

plot3d(omega(x,t),x=0..1,t=0..1);
################################

################################
restart:
a:=-1:
n:=3:
c:=2:
r:=0:
k_1:=0:
k_2:=0:
h:=1:

n:=3:
assume(0<=x and x<h):
assume(0<=t and t<h):
if a=1 then
omega:=(x,t)->piecewise(abs(x-c*t)<=2*n*(k_1-r)*Pi/(k_1*(n-1)),(sqrt(2*c*n/(n+1))*sin ((x-c*t)*(n-1)/(2*n)+r*Pi/k_1))^(2/(n-1)),0);
print(omega(x,t));
elif a=-1 then
omega:=(x,t)->(sqrt(2*c*n/(n+1))*sinh ((x-c*t)*(n-1)/(2*n)+k_2))^(2/(n-1));
print(omega(x,t));
end if:

plot3d(omega(x,t),x=0..1,t=0..1);

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