as the equation was not displayed i uploaded it again:

quad_eqn.docx

MaplePrime.mw

thanks

thank you.

actually V(x1) is the energy function. the original DE is:

m1*(gamma*rho+(gamma*sin(x1)^2-(sigma*cos(x1))^2)*diff(V(x1),x1)) = 
        -kappa*sin(x1);

we need to find V(x1) such that the following are satisfied:
- V has the minimum at x1=0.
- and m1>0. m1 could be constant or function of x1.

i have chosen m1=exp(x1) as this gives positive values over (0,2*pi).

if i chose m1=constant=gamma, then we get the following V which has maximum at x1=0.
V(x1) = kappa*arctanh((sigma^2+gamma^2)*cos(x1)/sqrt(gamma*(rho+gamma)*(sigma^2+gamma^2)))/sqrt(gamma*(rho+gamma)*(sigma^2+gamma^2))

so we want to choose m1 that satisfies the above conditions. 

thanks

thank you.

actually V(x1) is the energy function. the original DE is:

m1*(gamma*rho+(gamma*sin(x1)^2-(sigma*cos(x1))^2)*diff(V(x1),x1)) = 
        -kappa*sin(x1);

we need to find V(x1) such that the following are satisfied:
- V has the minimum at x1=0.
- and m1>0. m1 could be constant or function of x1.

i have chosen m1=exp(x1) as this gives positive values over (0,2*pi).

if i chose m1=constant=gamma, then we get the following V which has maximum at x1=0.
V(x1) = kappa*arctanh((sigma^2+gamma^2)*cos(x1)/sqrt(gamma*(rho+gamma)*(sigma^2+gamma^2)))/sqrt(gamma*(rho+gamma)*(sigma^2+gamma^2))

so we want to choose m1 that satisfies the above conditions. 

thanks

@Carl Love  the domain is 0≤x1≤2pi.

thanks

@Carl Love  the domain is 0≤x1≤2pi.

thanks

thank you,
the full equation is:

DE := (gamma*rho+(gamma*sin(x1)^2-(sigma*cos(x1))^2)*diff(V(x1),x1)) = -kappa*sin(x1)/exp(x1)

the values of the parameters are:
gamma=0.0048;
rho=0.0069;
sigma=0.0046;
kappa=0.2096.

can you please show me the solution as i could not evaluate the integral. if you can provide the solution here, can you please attach the maple file and send it to my mail: mryalat@gmail.com

thanks a lot,
mutaz

thank you,
the full equation is:

DE := (gamma*rho+(gamma*sin(x1)^2-(sigma*cos(x1))^2)*diff(V(x1),x1)) = -kappa*sin(x1)/exp(x1)

the values of the parameters are:
gamma=0.0048;
rho=0.0069;
sigma=0.0046;
kappa=0.2096.

can you please show me the solution as i could not evaluate the integral. if you can provide the solution here, can you please attach the maple file and send it to my mail: mryalat@gmail.com

thanks a lot,
mutaz