I have this solution that I don't quite understand
d(ro*pi*D^3/6)/d(t)=-kr*Cao*pi*D^2
from here I would have thought to separate the variables and integrate but the solution says
ro/2* d(D)/d(t) = -kr Cao
I guess my question is how are you able to do that? If you take the derivative...
Is it possible to define a function for an entire column in excel? I have data importing from a chemical process simulator and every time it populates a row it will insert a blank row and I need to copy my formulas. Can I make it so, for example, column B is always equal to Column A+something...
I need to solve 0=u[(d/dr)((1/r)*(d/dr)(r*Vo))] for Vo
the prof gets Vo=Co*r/2+C1/r
I don't get the same answer as him, does anyone know how to do this?
In part of a derivation they have, Integrate dx/(1-x) = (1-aW)^(1/2) dW
I get -ln(1-x) = (-2/3a)*(1-aW)^(3/2) but they say it's ln(1/(1-X)) = (2/3a)((1-(1-AW)^(3/2))
Can anyone tell me how they get that extra "1-"?
I'm trying to understand this one derivation but this one part keeps messing me up;
theta = tan^-1 (y/x)
r^2 = x^2 + y^2
d theta/ d x = y/ (x^2 + y^2) how did they get this line?
I keep struggling to find a solution to this IVP. We are supposed to use integrating factors
y'-(1/t)y=8t^2+te^t
t>0, y(1)=6
I get an integrating factor of (1/t) and general solution of y=4t^3+te^t+c but then i get e+2 for c. This doesn't seem correct to me, any suggestions?