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)