For the differential equation dy/dx=sqrt(y^2−36) does the
existence/uniqueness theorem guarantee that there is a solution to...
For the differential equation dy/dx=sqrt(y^2−36) does the
existence/uniqueness theorem guarantee that there is a solution to
this equation through the point
1.) (10pts) Consider the following differential equation:
(x^2)(dy/dx)=2x(sqrt(y))+(x^3)(sqrt(y))
a)Determine whether the equation is separable (S), linear (L),
autonomous (A), or non-linear (N). (An equation could be more than
one of these types.)
b)Identify the region of the plane where the Chapter 1 Existence
and Uniqueness Theorem guarantees a unique solution exists at an
initial condition (x0, y0).
2.(12pts) Consider the IVP: y'+y=y/t , y(2) = 0
For each of the functions y1(t)and y2(t)
below, decide if it is a solution...
Consider the differential equation dy/dx = y^2 + y - 2 (1)
Sketch its phase portrait and classify the critical points. (2)
Find the explicit solution of the DE.
Consider the first-order separable differential
equation
dy/dx = y(y − 1)^2
where the domain of y ranges over [0, ∞).
(a) Using the partial fraction decomposition
1/(y(y − 1)^2) = 1/y −1/(y − 1) +1/((y − 1)^2)
find the general solution as an implicit function of y
(do not
attempt to solve for y itself as a function of x).
(b) Draw a phase diagram for (1). Assuming the initial value y(0)
=y0, find the interval of values for y0...