Solve the Ordinary Differential Equation : xy'- y=2x^2

Solve the Ordinary Differential Equation 1 ) xy'- y=2x^2

Gravity, Gravitational Force, Gravity of Planets in the Solar System and Period of a Pendulum

Background Information: A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string). When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth ...continues

Statistical Information

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. ...continues

Equations

In the real world, what might be a situation where it is preferable for the data to form a relation but not a function? There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points: Fahrenheit Celsius Freezi ...continues

Inverse Laplace Transforms and Convolution Integral ( Theorem ) (4 Problems)

Find the inverse Laplace transform of the following: (a) 10/(s2+9) (b) 2e^-2s /(s+3) (c) .... (d) Find the inverse Laplace transform of F(s) using convolution integral where F(s) = .... Please see the attached file for the fully formatted problems.

Transfer Function from Voltage, Inductance, Resistance and Capacitance

A battery of voltage Vi is connected in series with a resistor of resistance R, an inductor of inductance L and a capacitor of capacitance C. If the output voltage across capacitor is Vo, derive the transfer function.

Matrices and Matrix Applications : Find the equivalent first-order system for a second order equation.

Find the equivalent first-order system (that is, find the matrix A and the vector R of dv/dx = Av + R) for the second order equation: u'' + (x^2)u' + (x^4)u = 1/(1+x^2) Please see the attached file for the fully formatted problems.

Linear Differential Equations : Solving by Change of Variables - Changing an Independent Variable

Please see the attached file for the fully formatted problems.

Legendre equation

(See attached file for full problem description)

General Solution to Homogeneous Differential Equation : (y^2 + yx)dx + x(^2)dy=0

(y^2 + yx)dx + x(^2)dy=0