Question

ODE's
Can someone please check to see if i have made any mistakes

Answer 1

Looks perfect to me. :)

Answer 2

are second ones non-linear???

Answer 3

i mean to say 1st ones b part.....

Answer 4

is this one (d)\[\frac{\text dy}{\text dx}=x\sec x\] linear in x?

Answer 5

no , i am talking about (b)?

Answer 6

ya (d) is linear......

Answer 7

(b) is nonlinear

Answer 8

b is not because the derivatives are to the power n

Answer 9

as far as i know a linear differential equation is one in which the required variable and its derivatives are not multiplied together

Answer 10

what about e?

Answer 11

like if y (dy/dx) was present,then it could be non linear

Answer 12

is 1.e) linear in x ?

Answer 13

non linear

Answer 14

no it's non linear i was just saying it could be classified as a bernoulli order one

Answer 15

in it ,dependent variable y is multiplied with its derivative

Answer 16

bernoulli nonlinear

Answer 17

if you divide it by

\[\frac{dy}{dx}+0y=xy^{-1}\]

bernoulli's equation is

\[y'+p(x)=q(x)y^n\]

Answer 18

my teacher is less into how to classify as much as how to solve each one

Answer 19

i was so mad i messed up on my test -.-

so i had something like this

\[c_1x^0+2c_2x^0+\sum f(x)\]

Answer 20

(e)\[y\frac{\text dy}{\text dx}=x\]\[\frac{\text dy}{\text dx}=xy^{-1}\]\[\text{1st order, 1st degree, nonlinear Bernoulli ODE } y(x)\]

Answer 21

and the sum reccurence was only for values c2 and above

Answer 22

oh i see

Answer 23

and i needed two linear solutions and i took the c_2 recurrence and multiplied by x... when in reality i should have had

y=1 and y = 2+sum

Answer 24

right?

Answer 25

because the linear solutions would be

\[c_1=1,c_2=0\]

but the sum only pulled out the values with c_2 which = 0

so you get

\[y=1x^0=1\]

Answer 26

gahh fail me lol

Answer 27

the other would be \[c_2=1,c_1=0\]

Answer 28

have i made all the corrections?