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 Please see attached file for full problem description.

Differential Equation questions

Problems: 1. Consider the IVP y' + p(t)y = q(t), y(0) = y0. Determine an input q(1) such that y(t) = y(0), for all that t (greater than or equal to) 0, is the the solution of the IVP. 2. Solve the IVP below and write the solution as the sum of the response to the initial data and the response to the input function. Give the largest t-interval on which the solution is defined: (FUNCTION1) 3. A hard-boiled egg is removed from a pot of hot water and set on the table to cool. Initially, the egg's temperature is 180F. After an hour the temperature is 140F. If the room's temperature is 65F, when will the egg's temerpature be 120F, 90F, 65F? (PLEASE SEE ATTACHMENTS FOR COMPLETE PROBLEMS ... click for more

Second order ODE

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

Consider the nonlinear differential equation

1. Consider the nonlinear differential equation attached a. Find the solution to this differential equation satisfying... (Please see attachment)

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 mercury will be present in the lake in the long run? 3. Supposed that in 1940 the power plant began contributing 8.5 grams pf mercury per year into the lake. In 2000 the plant reduced its pollution to 2 grams anually. In what year the will the mercury level fall below 120 grams?