Microsoft Word - Extra Credit.docx
MA 2A Extra Credit
1. Find the general solution for the following equation:
(x3 + y3 + 2xy) dx + (3xy2 + x2 + y3) dy = 0.
2. Find the solution of the equation !"
!#
+ 4xy= 2x with y(0) = 2.
3. If y(x) is a solution of y’ = x2 + xy + y with y(3) = 2, find an approximation for y(2.9)
using Euler’s method with h = -.05.
4. Suppose y(x) is a solution of y’ = (y XXXXXXXXXX – y) .
a. If y(0) = 0, what is the limit of y(x) as x approaches +¥ ?
. If y(0) = 10, what is the limit of y(x) as x approaches +¥?
c. If y(0) = 100, what is the limit of y(x) as x approaches +¥?
5. Find the general solution to !"
!#
= 2y + x + 5.
6. Find the general solution of y’’ = 5y’ + 6y where y is a function of x.
7. Find the solution of y” – 2y’ + y = 0 with y(0) = 3 and y’(0) = -2.
8. Find the general solution of y” = 3y’ +4x -5.
9. Find the general solution to x2y” + 7xy’ + 8y = 0.
10. Find two linearly independent power series solutions about the point 0 to:
y” – xy’ + 2y = 0.
11. Find L {f(t)} directly from the definition of the Laplace transform if
f(t) = 2t + 1 for t £ 1 and 1 for t > 1.
12. Find L {t5 }
13. Find L {t5 sin 3t}
14. Find L-1{ $%&
$'%(
}
15. Use the Laplace transform to solve y ′′ − 3y ′ + 2y = e3t , y(0) = 1, y′ (0) = 0.
MA 2A Extra Credit
16. Using eigenvalues, find the general solution to the following system of equations.
x’ = -6x + 2y
y’ = -3x + y
17. Using eigenvalues, find the general solution to the following system of equations.
x’ = -6x + 5y
y’ = -5x + 4y
18. Using eigenvalues, find the general solution to the following system of equations.
x’ = x + y
y’ = -2x - y