Determine if the following system has nay non-constant solutions that are bounded, i.e. do not run off to infinity in magnitude x’ = x(y – 1) y’ = y(x – 1) Explain in some detail, the reason for your answer.

Ordinary Differential Equation Determine if the following system has nay non-constant solutions that are bounded, i.e. do not run off to infinity in magnitude x’ = x(y – 1) y’ = y( ...continues

simple ODE

Consider the following system... Show that this system is a Hamiltnian system. Please see attached.

simple ODE

Find a third order Taylor polynomial approximation, centered at t=0 of the solution to... Please see attached.

Differential Equations exact solution

Determine if the following equation is exact. If it is, solve it. If not, try to solve it by finding an integrating factor. cosx + y(sinx)y'=0

Differential equations variation of parameters

Use variation of parameters to solve the differential equation y'''+4y'=cot2t (The y''' is correct) Please show complete work. Thanks

Differential Equations LaPlace tranform method

Use the LaPlace transform method to solve the initial value problem y'''+y''-2y'+y=cos2t, y(0)=1, y'(0)=0, y''(0)=-1 Please show all work! Thanks

General solution to a 2nd + 4th order DE

a) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t) find general solution to both the above and below b) y''+y=tcost

3rd order DE using Variation of Parameters

y"'+4y' = cot 2t variation of parameters to solve above equation.

elimination method 1

The following problem (attached) needs to be solved using the elimination method.

Second Order

Find general solution of a second order differential equation.