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 equatio ...continues

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 th ...continues

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 ...continues

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.

OED; IVP; Real-Value Solution; Solution Curves

y1: Find the general solution of the OEDs: y'''-3y"+3y'-y=0 y"=0 y"+y'-2y=0 5y"-10'=0 And about 8 other ODEs with IVP

Mortgage Differential Linear 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 ...continues

particular solution second orderODE

find a particular solution to: y'' + 6y' + 9y = (-11e^(-3t)) / (t^2 + 1)

particular solution second orderODE

find particular solution to: y'' + 25y = -20sec(5t)

second order ODE

find particular solution to: y'' + 25y = -20sec(5t)