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I don't understand how he goes from C1*e+C2*e^2 to 1/e-e^2 ..read more

Okay so I rewrite it as [math]y'' + [(y')^2 - 1]y' + y = 0[/math] So if I understand right damping is energy lost from the oscillation. So if there is no damping there will be an infinite oscillation. With that thinking a negative damping will cause an increasing amplitude of the sinusoid. 1.) When y'=-1,1 we get infinite oscillation. 2.) When -1 < y' < 1 we get negative damping and therefor increasing amplitude. 3.) When -1 > y' > 1 we get positive damping and therefor decreasing... Read more ..read more

My first instinct was to use the Energy Integral Lemma given from my book [math]t = \pm \int \frac{1}{\sqrt{2 (F(x) + K)}} dy + c[/math] K being a constant Which I feel like is sufficient but the solution manual provides the following. Which I don't understand and didn't even know that the chain rule could be used on function notation like this. I guess the s is a stand in for -t. Crazy that you can use the chain rule like this. Is what I did sufficient or... Read more ..read more

Learning to use Mathematical software, seems I properly integrated d^2y/dx^2-3dy/dx+2y=2x-3 and thus revealed the primitive y=C1e^x+C2^(e2x) then plugged in x=1 y=0 and did obtain C1e+C2e^2=-1 as Ayer's shows in Chapter 2 Problem 3 , but do not understand his "C1=-C2=1/(e^2-e)" I do however understand what follows, that C1e^x+C2E^2x+x will be y=x+e^x-e^2x/e^2-e that is if "C1=-C2=1/(e^2-e)" as he states ..read more

Trying to learn a Mathematical software, I follow Ayer's down the line on problem 3 of Chapter 2 until "When x=1 y=0: C1e+C2e^2-3 = 2x-3". My software says -2C1e-2C2e^2, which possibly could be just another way of stating his 'C1e+C2e^2=-1' however the most confounding part is that he further states "C1=-C2=1/(e^2-e)" which is .214 but doesn't appear to me to be simplification of any kind, my software shows C1=0 and C2=e^2/3. ANYBODY HAVE ANY IDEAS LOVE TO HEAR THEM ..read more

Hello everyone! I am looking for the needed technique for few days now and struggle to find it, hopfully I will manage to get help here. I have a system with no input, the system is represented by matricular differential equation. The system does not have any input, i.e. vector U=0 and therefore I dont have matrix B. I do have Matrix A, Matrix C and I know vectors x and y variables: dx/dt = Ax x(t=0) = x0 y = cx [Dimenssions: |A|=5x5 , |C|=3x5, |x| = 5X1 My question is - Is it possible... Read more ..read more

Can anyone solve dy/dx= 6e^y sin3x when y=0 and x=0. I cannot get the answer which is y=-ln|-2cosx+3 ..read more