Phase Lines

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Linear Equations

I am having problems understanding how to solve linear equations. For example, dy/dt = -4y + 3e^-t Can you solve this step-by-step so that maybe I can understand how to do it myself?

Linear Equations

I am having problems solving this linear equation. I think it's the sin that is throwing me off. Can you show me how to solve this? dy/dt = 2y + sin 2t

Linear Equations

Not sure how to solve this particular equation. I am finding linear equations to be a bit confusing. Can you show me how to do this one? dy/dt = y/2 + 4e^t/2

Total Differentials

I have 2 functions I would like to take the total differential of: I= I (R-PI) and C=C(Y-T, R-PI)) Where PI is Pie. If you can walk me through the process, that will help me better understand it and be able to work on other problems

Dependency Equation

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Use Laplace transforms to solve an initial value problem

Use Laplace transforms to solve the initial value problem y'' + ty' - 2y = 1, y(0) = 0, y' (0) =0. Because this equation does not have constant coefficients may need to use the frequency differentiation property of Laplace transforms ( L[(t^n)f(t)](s) = ((-1)^n)F^(n)(s) and the fact that if y(t) is a solution to this differenti ...continues

Proof with the frequency differentiation property of Laplace Transforms

Let f(t) be a function with L[f](s) = F(s). Use the fact that L[(t^n)f(t)] = ((-1)^n)*F^(n)(s) to show that L[t*f'(t)](s)=-s*F'(s) - F(s).

Modeling forces with a system

When one models a pair of conventional forces in combat, the following system arises x1’ -a -b x1 p x2’ = -c -d x2 + q The unknown functions x1(t) and x2(t) represent the strengths of opposing forces at time t. The terms –ax1 and –dx2 represent operational loss rates and –cx1 and –bx2 represent combat loss rates. The c ...continues

Ordinary Differential Equation

Find the particular solution of the following differential equation: 12(d^2y/dt^2)-3y=0 given that when t=0, y=3 and dy/dt=0.5 and could you explain the reasons for choosing y=e^(rt)