Question
(i) Find the general solution of the equation
d2 y
dy
+ 4 + 5y = 0.
2
dx
dx
(ii) Use the result of part (i) to nd the solution of
d2 y
dy
+ 4 + 5y = 2e3x ,
2
dx
dx
where y = 1 and
dy
= 3 when x = 0.
dx
Answer
(i) Use trial function y = Aekx
d2 y
Worksheet 7 Solutions, Math 53
Gradients and Optimization
Wednesday, October 10, 2012
1. Find the equation of the tangent plane and the normal line to the surface
x + y + z = exyz
at the point (0, 0, 1).
Solution
We can represent this surface by f (x, y,