the definition i have for a linear DE is that it is a DE that can be written in the form y' + P(x)*y = q(x). I am trying to rewrite the DE in that form, but it looks like I can't. If I can't, then according to the definition I have, the equation is not linear, and therefore not separable. But...
Homework Statement
The mass of a rocket, including a full chamber of fuel, is M. Its net mass without fuel is m. The products of combustion are ejected with velocity c. If the rocket starts from rest, derive Ciolkovski's formula.
Homework Equations
N/A. This is actually from differential...
Homework Statement
Solve 3xy^3 + (1+3x^2y^2)dy/dx=0 using integrating factors
Homework Equations
y' + p(x) = q(x)
The Attempt at a Solution
I'm having trouble putting the equation to y' + p(x) = q(x)
I distributed dy/dx so it becomes 3xy^3dy/dx + 1dy/dx+3x^2y^2dy/dx=0
But I...
Homework Statement
x^4 + x^3 + 2x - 4 = 0
Homework Equations
N/A
The Attempt at a Solution
x^4 + x^3 + 2x - 4 = 0
x(x^3 + x^2 +2) = 4
i don't know what to do with this. i tried to factor (x^3 + x^2 +2), but i don't know how. I also have a feeling that I am not doing this...
Homework Statement
A tin organ pipe decays with age as a result of a chemical reaction that is catalyzed by the decayed tin. as a result, the rate at which the tin decays is proportional to the product of the amount of tin left and the amount that has already decayed. Let M be the total amount...
Homework Statement
Use separation of variables to solve (x+2y)y'=1 y(0)=2Homework Equations
u=2y+x >>I did not know how to start this, so i looked at the back of the book and it said to use that substitution
y=(u-x)/2, du=2dy+dx, dy=(du-dx)/2
The Attempt at a Solution
so i got the following...