Consider the differential equation
2y^2+10y+12 = t+e^t
Find the complementary function and particular integral. Hence
write down the full general solution
Differential Equations
22. Solve each of the following systems of equations.
(c) (D-2)x=0; -3x+(D+2)y=0; -2y+(D-3)z=0
I got x=c1e2t, y= 3/4
C1e2t + C2e-2t by using
diffieq method d/dx(ye2t) =
3C1e2t....., but the right answer is
x=4c1e2t, y= 3C1e2t
+ 5C2e-2t , z= -6C1e2t
-2C2e-2t+C3e3t
I want to know where 4 came from, and please do not use matrix
system.
2. Given the System of Equations:
3x+2y+z+20w= 6
x+2y+z+10w=0
x+y+z+6w=2
2x+2y+z+15w=3
a) Use your calculator to solve, leaving solution in parametric
form
b) Find the specific solution when y = 6
c) Perform, BY HAND, a full check of this particular
solution
Expand the function f(z) = (z − 1) / z^ 2 (z + 1)(z − 3) as a
Laurent series about the origin z = 0 in all annular regions whose
boundaries are the circles containing the singularities of this
function.
3. Solve the following system of equations.
5x- y+ z= -4
2x+ 2y-3z= -6
x-3y+ 2z= 0
Select the correct choice below:
A. There is one solution. The solution is
( ).
B. There are infinitely many solutions. The solutions
( ,z)
C. There is no solution.
4. The total number of restaurant-purchased meals that the
average person will eat in a restaurant, in a car, or at home in
a year is 150. The total number of these meals...
1A) Use surface integral to evaluate the flux
of
F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2
1B) Use the Divergence Theorem to evaluate the
flux of F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2