Sifferential 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

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 together with initial condition for the balance B(t) she owes the bank at time t. • What is the maximum mortgage Miss X can take that she can replay in finite time? • If the repayment period is 25 years, what is the maximum mortgage Miss X can take? 2) Consider the functions 1. • Write the Wronskian of these functions • Evaluate the wronskian • Are these f... click for more

Linear Differntial Equations

1) Consider the equation... • Find its general solution. • Find the particular solution of this equation satifying the initial condition. 2) Find the general solution of the differential equation... • Prescribe any concrete initial data for twhich this equation has a unique solution. • Find the particular solution of this equation satisfying the initial condition stated in the part above. Please see attached for all equations.

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

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.