Inroductory differential equations (1 Viewer)

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1. The problem statement, all variables and given/known data
A function y(t) satisfies the differential equation: dy/dt= y^4-7y^3+6y^2. What are the constant solutions to the equation?


2. Relevant equations
dy/dx= g(x)*f(y) --> INT([1/f(y)]dx/dy)=INT(g(x))


3. The attempt at a solution
My first attempt was to factor out a y^2 term and divide it to the other side and take the integral. After a couple more steps, I realized this was not correct. My second attempt was to factor the differential equation into two factors and divide one of the factors to the other side, but this always leaves me integrating a factor with y's with respect to t. I cannot figure out how to attack this problem.
 
If you want the general solution why dont you just multiply both sides by dt and then divide by y^4-7y^3+6y^2.

That would give you

dy/ y^4-7y^3+6y^2 = dt

So integrate the left side with respect to y, and the right side with respect to t.
 

HallsofIvy

Science Advisor
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1. The problem statement, all variables and given/known data
A function y(t) satisfies the differential equation: dy/dt= y^4-7y^3+6y^2. What are the constant solutions to the equation?


2. Relevant equations
dy/dx= g(x)*f(y) --> INT([1/f(y)]dx/dy)=INT(g(x))


3. The attempt at a solution
My first attempt was to factor out a y^2 term and divide it to the other side and take the integral. After a couple more steps, I realized this was not correct. My second attempt was to factor the differential equation into two factors and divide one of the factors to the other side, but this always leaves me integrating a factor with y's with respect to t. I cannot figure out how to attack this problem.
You are NOT asked to find a general solution! You are only asked to find the constant solutions. if y is constant then dy/dx= 0.

Can you solve y^4-7y^3+6y^2= 0?
 
oh wow good catch Ivy! Maybe i need to get some glasses... hah...

Do what Ivy said!
 

HallsofIvy

Science Advisor
41,626
821
Time to stop doing it?
 

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