@tomleslie 

Many Thanks.

I'll appreciate if assist me to answer two following questions:

1- Since my question was about how to solve a first-order ODE [diff(A(x),x)^2+V(A(x))=0],  I ignored one of the ICs, but I encountered Maple an error message ('unable to convert to an explicit first-order system'). How can I remove it?

2- How can I find another point (except x=0) like x1<>0 where A(x) satisfies the following two conditions in that point?

A(x1)=0

dA(x1)/dx=0.

Sincerely.

For the first question, assume

V(A):=M^(2)-M*(M^(2)+2* A)^(1/(2))+mu1*(M^(2)*mu+s1)-mu1*((M^(2)*mu)/(2))^(1/(2))*{[(M^(2)*mu+3*s1-2*A)+sqrt((M^(2)*mu+3*s1-2*A)^(2)-12*M^(2)*mu*s1)]^(1/(2))+(4*M^(2)*mu*s1)*[(M^(2)*mu+3*s1-2*A)+sqrt((M^(2)*mu+3*s1-2*A)^(2)-12*M^(2)*mu*s1)]^(-3/(2))}-(2*mu2)/((3*q-1))*{[1-(q-1)*A]^((3*q-1)/(2*q-2))-1}-(2*mu3)/(s*(3*q1-1))*{[1+s*(q1-1)*A]^((3*q1-1)/(2*q1-2))-1};

where q1=0.4, q=0.4, s1=0, mu=2, mu1=0.7, mu3=0.2, s=0.5, M=1.9109 and mu2=1+mu3-mu1.

@tomleslie 
Thanks Sir!

@tomleslie 

Thank you very much.

It works very well.

Only a little question, the solutions are obtained in term of q1(X), how do I get them  in term of pphi1(X)?

@raj2018 Is there anyone who can help me?
Thank you if anyone can help me find the answers to my questions.

@Carl Love In fact, the quantities u and w were expressed
asymptotically as a powers in epsilon about the equilibrium state as:

w=w0+epsilonw^(1)+epsilon^2w^(2)+...., where w^(1), w^(2), ... are the first- and the second- order of quantity W. 

Therefore, I want to solve the following set Eqs. for different orders of epsilon:

For example, for epsilon^1:

(1)              du1/dt+u0d*(W1)/dx+W0d*(U1)/dx=0

(2)              dw0/dt+w0dw1/dx=0

Of course, as I said, the change of the variable (x,t->X,T)must be applied first.