Integrating Factors

Use the five steps of the Method of Integrating Factors to find the general solution of each linear ODE (hint: write ODE in normal linear form): y' - 2ty = t y' = sin(t) + y*sin(t) (PLEASE SEE ATTACHMENT FOR COMPLETE PROBLEM)

Solving an IVP Long-Term Behaviour of the Solution

Problem: First find the general solution of the linear ODE in each IVP by following the steps of the procedure. Then use the initial condition to find the solution of the IVP. Discuss that solution's qualitative behaviour as t --> +(SYMBOL). Give the largest t-interval on which the solution is defined: y' + 2y = 3, y(0) = 1 ...continues

Second Order ODE

Find y as a function of x if (x^2)(y'')-7xy'-9y = x^2 y(1)=6 y'(1)=8

Solution to Nonlinear Differential Equation

Please see the attached file for the fully formatted problems. 1. Consider the nonlinear differential equation attached a. Find the solution to this differential equation satisfying y(0) = y0 where y0 does not equal +/- 1. What is the solution if y0 = +/-1. b. What happens to the solution as t--> infinity for y0 > -1? ...continues

Mercury pollution in a lake

A lake contains 60 million cubic meters (2MCM) of water. Each year a nearby plant adds 8.5 grams of mercury to the lake. Each year 2MCM of lake water are replaced with mercury-free water. 1. What is the differential equation that governs the amount of mercury in the lake? 2. According to your differential equation how much m ...continues

Leaky bucket

3. Leaky bucket: A bucket in the shape of a cylinder has a small hole in its bottom, through which water is leaking. Let the height of the water in the bucket be h(t), let A be the cross sectional area of the bucket and a the area of teh small hole. We want to find out how long will it take the bucket to empty (see attachment fo ...continues

Solution to Second Order ODE

Find solution of y'' + 6y' = 80exp((2)t)) with y(0) = 8 and y'(0)=5

Solution to Second Order ODE

Find solution of: y'' - 2y' + y = 16exp((5)t) y(0)=1 y'(0)=6

Solve a Second Order ODE

Find solution of y'' + 8y' = 896sin(8t) + 640cos(8t) with y(0)= 4 and y'(0)=9

Second Order ODE

Use method of undetermined coefficients to find one solution of: y'' - 9y' +24y = (7)exp((6)*t)