Matrices - Subspaces

From the attached jpeg file please solve nos. 58, 60, 62 & 64 only.

Differentiation of a MGF

Please see attachment.

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

I attached the problem. Please help me to solve it with detailed explanation if needed. Thanks

Solving a first order linear equation

I am studying this subject alone and will require help along the way. I hope that you can assist me now and in the future. 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 conti ...continues

Suppose that p and q are continuous on some open interval I

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

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%

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 equatiion: d^2/dt^2 + 4dy/dt + 104y = 832 y(0) = 0; y'(0)=0

2nd order differential equation

Hi, I attached the problem. Please help me providing detailed solution with explanation. Thanks Dr. Xiong