Slope Fields

Suppose the constant function y(t) = 2 for all t is a solution of the differential equation dy = f(t,y). dt (a) What does this tell you about the function f(t,y)? (b) What does this tell you about the slope field? In other words, how much of the slope field can you sketch using this information? (c) What does this ...continues

Differential Equations : Phase Lines

Suppose you wish to model a population with a differential equation of the form dP/dt = f(p), where P(t) is the population at time t. Experiments have been performed on the population that give the following information: • The population P = 0 remains constant. • A population close to 0 will decrease. • A population of P = ...continues

Integration by Substituton

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?

Solving Differential 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 Pi. 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, Feasibility Analysis and Row Reduced Echelon Form

4. The Volta Battery Company manufactures AA, A. C, and D batteries in each of four plants. The daily production (in 1000's) for the four plants is given the following table: [TABLE] (a) The vectors that represent the production at the various plants are not linearly independent. Show this and find a dependency equation. (b) ...continues

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).

Systems of Differential Equations : Modeling a Battle between Two Armies

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