Homework Help: Solving an ODE

cragar · Aug 26, 2012

1. The problem statement, all variables and given/known data
Ay'+Bxy=Cy
y=f(x)
A,B,C are real constants
3. The attempt at a solution
This kinda looks like a Bernoulli equation but not really.
I thought about using an integrating factor but there is function of x on the right side.
If I tried undetermined coefficients what would my guess function be.

elvishatcher · Aug 26, 2012

It seems like you could solve this by first manipulating to get [tex]y' + \frac{Bx-C}{A}y = 0[/tex] at which point you now have an ODE of the form [tex]y' + P(x)y = Q(x)[/tex] and there is a general way to solve such ODEs.

cragar · Aug 26, 2012

where Q(x)=0 and then use an integrating factor.

elvishatcher · Aug 26, 2012

Yep, seems like that oughta work

cragar · Aug 27, 2012

if you do that you get y=0.

ehild · Aug 27, 2012

elvishatcher said: ↑

It seems like you could solve this by first manipulating to get [tex]y' + \frac{Bx-C}{A}y = 0[/tex]

or [tex]y' = -\frac{Bx-C}{A}y [/tex]

which is separable. [tex]\frac{y'}{y} = -\frac{Bx-C}{A}[/tex].

ehild

cragar · Aug 27, 2012

wow cant believe I missed that , thanks for the help
ok so I would get
[itex] ln(y)= \frac{-1}{A}(\frac{Bx^2}{2}-Cx)+F [/itex]
F= integration constant
then I just raise each side to e and I will have y

ehild · Aug 27, 2012

Exactly. It will be a bit simpler if you eliminate the minus sign in front of the parentheses,

[tex]\ln(y)=\frac{1}{A}(Cx-B\frac{x^2}{2})+F[/tex]

ehild