CHE 527 Advanced Applied Mathematical Analysis in Chemical Engineering Fall 2006
Homework 3
Due in class on Thursday, September 14.
1. Given that y= 0 at x= 0, find yat x= 2 for a process governed by
dy
dx =x+y .
2. Consider the quadratic f(x) = x2+ 3x+ 1 = 0. Show that Newton’s method can be used to find both
roots by using different initial guesses.
3. The following differential equation arises in the analysis of convective heat transfer from a sphere:
(1 −x2)·g2·dg
dx −x·g3= 2 .
Solve this equation subject to the requirement that g(x) remain finite for all −1≤x < 1. Hint:
d(g3)
dx = 3g2dg
dx .
4. A brass ball-bearing initially at 200oC is dropped into water at 20oC at t= 0 and allowed to cool.
If it takes 5 minutes for the ball to cool to 50oC, how long does it take to cool to 30oC? Hint: Use
a constant heat-transfer coefficient in the water surrounding the ball, and note that the ball has very
high conductivity.
5. Find the solution to the initial-value problem:
d2y
dx2−2dy
dx + 2y= sin(x)
with y(0) = 1 and y0(0) = 0.
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