Week 7-10 (intergration)

Question 1

intergration by parts

Answer 1

S du/dx V = VU - S dv/dx U

Question 2

important indentity

Answer 2

cos^2 + sin^2 = 1

cosh^2 - sinh^2 = 1

Question 3

intergration using cosh(u)

Answer 3

when
1/sqrt(x^2 -1)

let x = cosh(u)

Question 4

Intergrating factors(first order ode)

Answer 4

I(x) = e^(S p(x) dx)

y = 1/(I(x)) * (S I(x)r(x) dx + C)

Question 5

For constant coefficients (first order ode)

Answer 5

yh = Ae^kx
do lambda thing to solve it

yp = Guess

Question 6

For constant coefficients (second order ode)

Answer 6

same thing

Question 7

boundary problem

Answer 7

just sub in initial conditions,

Question 8

eigen value

Answer 8

If you are given a parametric ode, then find eigen values and vectors

Question 9

eigen value repeated vales

Answer 9

just do the same thing

Question 10

complex eigen values

Answer 10

1. first do normal thing
2. solve for C
3. expand the e^1+i