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# Are 1st order linear differential equations in the general form need to be y always? watch

1. Or is y^2 ascpcetiable etc.
2. (Original post by Mihael_Keehl)
Or is y^2 ascpcetiable etc.
y' + yf(x) + g(x) =0 only

or perhaps special cases such as
y' + yf(x) +yn g(x) =0, except n=-1, BERNOULLI
y' + f(y)/x +g(y) =0 TREAT x and y THE OTHER WAY ROUND
3. (Original post by Mihael_Keehl)
Or is y^2 ascpcetiable etc.
It has to be , if it's not then it's a non-linear DE.
4. (Original post by TeeEm)
y' + yf(x) + g(x) =0 only

or perhaps special cases such as
y' + yf(x) +yn g(x) =0, except n=-1, BERNOULLI
y' + xf(y) +g(y) =0 TREAT x and y THE OTHER WAY ROUND
Bernoulli DE's aren't linear.
5. (Original post by TeeEm)
y' + yf(x) + g(x) =0 only

or perhaps special cases such as
y' + yf(x) +yn g(x) =0, except n=-1, BERNOULLI
y' + xf(y) +g(y) =0 TREAT x and y THE OTHER WAY ROUND

I kind of meant like in this example:

Mr S leaves his final answer (general solution) in terms of 2y^2 etc. do you not need to isolate y?

Thank you though,
6. (Original post by Mihael_Keehl)

I kind of meant like in this example:

Mr S leaves his final answer (general solution) in terms of 2y^2 etc. do you not need to isolate y?

Thank you though,
this is a different type of ODE known as homogeneous in x and y
7. (Original post by Mihael_Keehl)

I kind of meant like in this example:

Mr S leaves his final answer (general solution) in terms of 2y^2 etc. do you not need to isolate y?

Thank you though,
final answer can be any form if one is not specifically asked.

this type of equation however is called homogeneous in x and y
8. (Original post by TeeEm)
this is a different type of ODE known as homogeneous in x and y
(Original post by TeeEm)
final answer can be any form if one is not specifically asked.

this type of equation however is called homogeneous in x and y

May I ask you in your experience have you found that 1st order des 2nd order des are common in STEP?
9. (Original post by Mihael_Keehl)

May I ask you in your experience have you found that 1st order des 2nd order des are common in STEP?
I have almost no experience in STEP, but former students of mine that have done STEP, said thee is always an ODE in STEP (I think in STEP II)

Nevertheless ODE solving is very important for practical reasons as well as "building tools/building intelligence" reasons
10. (Original post by TeeEm)
I have almost no experience in STEP, but former students of mine that have done STEP, said thee is always an ODE in STEP (I think in STEP II)

Nevertheless ODE solving is very important for practical reasons as well as "building tools/building intelligence" reasons
great thank you

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