Solve a 2nd order ODE.

Use methods of undetermined coefficients to find one solution of: y'' + 2y' +2y = (10t+7)e^(-t)cos(t)+(11t+25)e^(-t)sin(t)

Ordinary Differential Equation : Change of Variables

Solve {see attachment} for y(x) using the change of variables z = y + x.

Gompertz Equation

2. The Gompertz equation y'(t) = y[a-b*ln(y)] is an important model for avascular tumor growth. In the avascular growth phase, tumor cells obtain nutrients directly from the surrounding tissue. (The transition from avascular to vascular growth is marked by the onset of angiogenesis, the formation of blood vessels, which are ...continues

Initial Value Problem - IVP (Euler's Method)

3. Consider the initial value problem (IVP): y'(t) = y^2 y(0)=1 Approximate y(1) using Euler's method and step sizes of 0.25. Perform these calculations by hand (using a calculator for arithmetic is ok). What is the true value of y(1)?

Initial Value Problem (IVP); Euler's Method; Step Sizes

4. Consider the initial value problem (IVP): y'(t) = 3+t+y y(0)=1 a) Approximate y(1) using Euler's method and step sizes of 0.2. Perform these calculations by hand. What is the exact value of y(1)? b) Use the computer (e.g. ODE Architect, ODE Toolkit, or your own program) to approximate y(1) using step sizes of 0.1, 0.05, ...continues

Solve Three Differential Equations

Find the general solution of the following system of differential equations: i.e. 1) dx/dt = x-2y-t2 (FOR COMPLETE PROBLEMS PLEASE SEE ATTACHMENT)

Differential Equations : Rate of Change Application Problem and Wronskian

1) Miss X would like to take out a mortgage to buy a house in Leicester. The bank will charge her interest at a fixed rate of 6.1% per year compounded continuously. Miss X is able to pay money back continuously at a rate of £6000 per year. • Make a continuous model of her economic situation, i.e. write a differential equation ...continues

Linear Differential Equations

1) Consider the equation... • Find its general solution. • Find the particular solution of this equation satisfying the initial condition. 2) Find the general solution of the differential equation... • Prescribe any concrete initial data for which this equation has a unique solution. • Find the particular solution of th ...continues

Differential Equation (DE); Initial Value Problem (IVP)

Consider the differential equation: r^2*R"+r*R'-R=0 a) Find all values of n for which the function R=r^n is a solution to the differential equation. Do this by substituting {the solution into the DE and seeing which values of n will make the equation true. b) Solve the initial-value problem (IVP) with R(1)=2 and R'(1)=0 ...continues

Taylor Series

Recall the Taylor series Sum(x^n/n!). The same series can be used to define e^z for a complex number z=a+bi. Use the Taylor series to show that exp(iy) = cos(y) + i sin(y) for any real number y. To do this substitute iy into the series and compute several terms. Look for patterns.