Question 1

2.6) If a DE is Not exact, we find __________________?

Accepted Answer

intergrationg factor

Question 2

2.6)If y is independent then the formula

Accepted Answer

p(x)=My-Nx/N

Question 3

2.6) If y is independent the the intergrating factor

Accepted Answer

u(x)=e^∫p(x)dx

Question 4

2.6) if x is independent then the formulal

Accepted Answer

q(y)=Nx-My/M

Question 5

2..6) if x is independent then the intergrating factor

Accepted Answer

u(y)=e^∫q(y)D\dy

Question 6

5.1) Standered form of a second order linear

Accepted Answer

y"+p(x)y'+q(x)y=g(x)

Question 7

5.1)A second order linear ODE is said to be homogeneous if

Accepted Answer

g(x)=0

Question 8

5.1) The Wronskian W(x) of {x,y}

Accepted Answer

W(x)=|x  y |
              |x' y'|

Question 9

5.2) Step One of solving a homogeneous DEs with constant coefficients

Accepted Answer

switch it into the corsopding characteristic equation: ar^2+br+c=0

Question 10

5.2) Step Two of solving a homogeneous DEs with constant coefficients

Accepted Answer

FInd the determinant, using the formula D=b^2 - 4ac

Question 11

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D>0 then "r" =?

Accepted Answer

r=r1,r2.

Question 12

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D>0 then what are the root/s?

Accepted Answer

two distinct real roots

Question 13

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D>0 then the solution will be

Accepted Answer

y=C1 e^(r1x) + C2 e^(r2x)

Question 14

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D=0 then "r"= ?

Accepted Answer

r=r1

Question 15

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D=0 then what are the root/s?

Accepted Answer

There is a repeated real root of r1

Question 16

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D=0 then what will the solution be?

Accepted Answer

y=e^(r1x) (C1+C2)(x)

Question 17

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D<0 then "r"= ?

Accepted Answer

r=ƛ±iw

Question 18

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D<0 then the root/s are?

Accepted Answer

There are two distinct roots complex roots.

Question 19

5.2)Step Two of solving a homogeneous DEs with constant coefficients: If D<0 then the solution will be?

Accepted Answer

y= e^(ƛx) (C1 cos(wx) +C2 sin(wx)

Question 20

5.2)Step Three of solving a homogeneous DEs with constant coefficients: What is the third step?

Accepted Answer

Determine the arbittrary values C1, C2 by solving IVP's.

Question 21

5.3) Nonhomogeneous second order linear DE form?

Accepted Answer

y" + p(x)y' +q(x)y =g (x)

Question 22

5.3) Nonhomogeneous second order linear DE general solution?

Accepted Answer

Y=C1 Y1(x) +C2 Y2(x) + Y(x)

Question 23

5.3)Step One of solving  Nonhomogeneous second order linear DE ?

Accepted Answer

Find the generall solution called the complementary solution of the corresponding homogeneous equation

Question 24

5.3)Step Two of solving  Nonhomogeneous second order linear DE (a)?

Accepted Answer

Find a particular solution y(x) of the nonhomogeneous Eq. you find this by making an intial guess about the form of the particulatr solution Y(t).

Question 25

5.3)Step Two of solving  Nonhomogeneous second order linear DE (b)?

Accepted Answer

You  Set up  the inital guess with the chart in slides. the we sub Y(x) into the nonhomomgenous Eq. and determine the constants

Question 26

5.3)Step Three of solving  Nonhomogeneous second order linear DE ?

Accepted Answer

The solution is y(x) = yc(x) + Y(x) where yc comes from step1 and Y from step two

Diff EQ. Test#2

2.6-5.5

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