Differential Equations

For each of the following ordinairy differential equations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous. a) df/dx +f^2=0 (See attachment for all questions)

Solve the ODE (Integrate)

Find the explicit solution to the ODE 2yy'=(1+y^2) subject to y(0)=4. What is the solution if y(0)=-4? *(Please see attachment for proper citation of symbols and numbers)

Ode (Boundary Condition, Implicit and Explicit Solutions)

Consider the ODE y' = y2/x subject to the boundary condition y(1)=1. Find an implicit solution of the form H(x,y) = constant, then find an explicit solution of the form y=y(x). What is the largest x-interval on which the solution is defined? *(Please see attachment for proper citation of symbols and numbers)

Solving an ODE

Find all solutions to the ODE yy'= (1-y^2) sin x. (When dividing by 1-y^2, be careful that you don't lose any solutions). NOTE: y2 = y squared Please see attached file for full problem description.

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

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 ...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

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 m ...continues