Question

can someone please help me with solving ODE's.
I can't seem to understand when to use separation of variables or integrating factor.

Answer 1

\[\frac{ dy }{ dx }+2xy=x\]

Answer 2

for separation of variables you need all y's on the left and all x's to the right and then integrate both sides

h(y) dy = f(x) dx

Answer 3

for this question i used integrating factor instead of separation of variables. i just don't know which method to use when.

Answer 4

for integrating factor, your equation needs to be in the form of
\[\frac{dy}{dx} + p(x)y =q(x)\]

Answer 5

wait let me recheck that formula

Answer 6

ok it's good

Answer 7

integrating factor seems to be the best choice on here.. your equation looks like it's in that form

Answer 8

dydx+2xy=x for this question how can you can tell which method to use?

Answer 9

i used integrating factor but apparently the solution is by separation of variables. i'm confused.

Answer 10

To use integrating factor your equation must be in the form
\[\frac{dy}{dx} + p(x)y =q(x) \]
for separation of variables you should be able to have all y's on the left and all x's on the right. YOur equation should look like this...
h(y) dy = f(x) dx
maybe manipulation to the original equation must be done and then use separation of variables

Answer 11

\[\frac{ dy }{ dx }+2xy=x \] try subtracting 2xy on both sides and factor out an x

Answer 12

yeah i did that and i got the answer. but i confusion lies when i the the question was in the form of integrating factor, so i used the integrating method. however the solution was with method of separating variables. my question is without knowing how they want us to solve the question using which one of 2 methods. Becoz i get different solutions with both methods

Answer 13

you are supposed to get the same solution regardless of what method you are using

Answer 14

really? so that means i'm something wrong in my solution

Answer 15

there's 5 variations of solving first order odes
exact, substitution, homogeneous, separation of variables, and integrating factor. All of these methods produce the same answer... it's just that some methods are easier to do than others.

Answer 16

same thing applies to second order odes
method of undetermined coefficients, laplace transform, and variation of parameters all give out the same solution.. but again one method is easier than the other.

Answer 17

oh i see, i'll try doing them again. Thanks for clarifying :)

Answer 18

I'm going to go eat dinner. This is a separable equation btw... sometimes you have shift terms first before we see a h(y) dy = f(x) dx format
just like how subtracting 2xy and factoring an x made it closer to achieving h(y) dy = f(x) dx format. The problem is the left side is always the jerk and the right side is always nice.