First Order Differential Equations

1. In the following, represent the situation pictorially and deduce the governing 1st order differential equations and initial condition for the quantity in question. a) A tank, containing 300 gallons of pure water initially, is emptied out in the following fashion. A salt solution of concentration ½ lb of salt per gallon is ...continues

XieCorp is a pc solutions provider that is looking to expand its operations. - Balance Income Statement

XieCorp is a pc solutions provider that is looking to expand its operations. Currently it has $500K (K=thousand) to invest in an upgrade in facilities. The goal is the hire additional staff to acquire new customers. Last year 20XX XieCorp made $13M (M=million) in total revenues. Their expenses were 65% of revenue and they were t ...continues

Differentiation of a Moment Generating Function

m’(t) = (μ+tσ²) exp {½ t²σ² + μt} m’(t) = (μ+tσ²) exp {½ t²σ² + μt} + σ²exp {½ t²σ² + μt} m’’(t) = ?? Please help

Second Order Ordinary Linear Differential Equations with Constant Coefficients

1). Given the differential equation for 1. L[y]= y''+2by'+b2y = exp(-bx)/x2, x>0 ; a) Find the complementary solution of (1) by solving L[y] = 0. b) Solve (1) by introducing the transformation y[x]= exp(-bx) v(x). into (1) and obtaining and solving completely a differential equation for v(x) . Now identify the part ...continues

Second Order Linear Equations : Mechanical Vibration

Please see the attached file for the fully formatted problems.

First order linear differential equations

To begin with, I have an example problem that asks to find a complete solution for: y'+ 2xy = x The text says to multiply both sides by e^int a(x) dx In this case, that equals e^x^2 It then continues by multiplying. 1) e^x^2 * y' + e^x^2 * 2xy = e^x^2 * x or 2) [e^x^2 * y]' = x * e^x^2 I do not understand h ...continues

Fundamental Set of Solutions to an ODE

Suppose that p and q are continuous on some open interval I, and suppose that y1 and y2 are solutions of the ODE y'' + p(t)y' + q(t)y = 0 on I. (a) Suppose that y1, y2 is a fundamental set of solutions. Prove that z1, z2, given by z1 = y1 + y2, z2 = y1 − y2, is also a fundamental set of solutions. (b) Prove that i ...continues

Using substitution to simplify an ODE

Let a, B be constants. Consider the ODE y'' + (a/x)y' + (B/x^2)y = 0 on the half-line x belongs to (0,infinity). (a) Make the substitution t = ln(x) and write the ODE with independent variable t. (b) From what you know about constant coefficient ODEs, separate the problem into three cases according to the values of a and B ...continues

Capital Gains on Stock

Suppose FPL will pay an annual dividend of $2.48 in 1994, and assume the market risk premium (RM – Rf) is 7.5% and the risk free interest rate is 7.3% (the current yield on 30-year T-bonds from Exhibit 8), and FPL Group Inc. stock is selling at $34 per share, what is the expected capital gains yield of FPL stock? (The total retu ...continues

Solving differential equations with complex numbers

I having problem with the following equation: d^2/dt^2 + 4dy/dt + 104y = 832 y(0) = 0; y'(0)=0