Homework Statement
Calculate the molar volume using the van der Waals equation of a gas at P=3000psia, T=60F. The critical pressure and temperature, Pc and Tc, are Pc=408psia, Tc=504F.
Homework Equations
The given van der Waals equations(s):
(P+a/Vm^2)(Vm-b)=RT ----(1)...
Bernoulli -- Find the general solution
Homework Statement
Find the general solution of:
y'+xy=xy^3
Homework Equations
Bernoulli's Equation
The Attempt at a Solution
y'+xy=xy^3
(y^-3)y'+x(y^-2)=x
Let v=(y^-2), thus v'=((-2y^-3)y'
Then,
-v'/2+xv=x
Multiply...
Grr! Yes, thank you!
I notice I make many silly mistakes when I rush through.
So, it's ...+30y = C :]
Thanks a BUNCH! I know it might be simplistic but our professor stressed how easy it was and just did one example (without the constant).
So, not so bad after all.
Again, thank...
Hehe, yes, I did in fact forget :)
I reposted with my answer.
y'=-x/5(y-3)
(y-3) dy = -x/5 dx
y2/2 - 3y = -x^2/10 +C
10*(x^2/10 + y^2/2 - 3y) = C
Ans: x^2 + 5y^2 - 30y = C (?)
Oops! I forgot what I was doing here. Back to business:
y'=-1/y'
Don't lose hope on me, I'm just burned out.
I'm going to try this on paper.
Thanks for the help thus far! :)
Or, taking a different route (inspired by your initial reply);
C=(y-3)/x^5
Sub'd into y'
y'=5x^4((y-3)/x^5))
y'=5/x(y-3)
1/(y-3) dy = 5/x dx
ln(y-3) = 5*ln(x) + C
y-3=x^5 + C
...but this still doesn't look right to me; unless I'm missing something.
I apologize; I just edited the post.
Given:
y=C*x^5 - 3
Solution for C:
C=y/x^5 + 3
Then, as shown above, I sub'd in the value for C in the y':
y'=5x^4(y/x^5 + 3)
y'=5y/x + 15x^4
Now, I can't factor out a "y" to make this D.E. separable.
Hello, forum! I'm a newbie here. I've been visiting this site for a while but just recently joined. Anyways, I was wondering if anyone could help with this problem. I can find the orthogonal trajectories, however, this one is killing me because there is a constant. Allow me to type it below...