2nd order ODE

find particular solution to y'' - 8y' +16y = 19.5e^(4t)

second order ODE

find a particular solution to y'' + 5y' +4y = -13te^(3t)

homog. 2nd order ODE

find y as a function of x if: (x^2)(y'') + 19xy' +81y = x^2 y(1) = 9 y'(1) = -3 Hint: First assume that at least one solution to the corresponding homogeneous equation is of the form . You may have to use some other method to find the second solution to make a fundamental set of solutions. Then use one of the two metho ...continues

2nd order ODE

find a particular solution to the differential equation: y'' - 2y' -15y = 450t^3

2nd order ODE

find a particular solution to the differential equation: y'' - 2y' -15y = 450t^3

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