convert the second order differential equation x" t + 2x' t - 3x t = x into 1st order

[mfm12a]

convert the second order differential equation x" t + 2x' t - 3x t = x into 1st order

1. Convert the second order differential equation
   x′′(t) + 2x′(t) − 3x(t) = x(t)3
   into a first order system in terms of x and v where v = dx/dt. Take note that this equation isnonlinear!
   
   
   
   1. (a) Show your work in converting the equation to a first order system below.
      
   2. (b) Use Maple to plot the vector field associated with the first order system.
      
   3. (c) Find all equilibrium points.
      
   4. (d) Use Maple to determine the phase portrait of the system showing enough solutions to determinethe overall solution behavior.
      
   
   
   
   

 

[Deleted member 4993]

2. Convert the second order differential equation
   x′′(t) + 2x′(t) − 3x(t) = x(t)3
   into a first order system in terms of x and v where v = dx/dt. Take note that this equation isnonlinear!
   
   
   2. (a) Show your work in converting the equation to a first order system below.
   3. (b) Use Maple to plot the vector field associated with the first order system.
   4. (c) Find all equilibrium points.
   5. (d) Use Maple to determine the phase portrait of the system showing enough solutions to determine the overall solution behavior.
   
   

You have posted ~9 problems without showing one line of original work!!

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