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...

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 of the IVP. (Answer is Yes or No, but show, or explain, briefly how you decided for each.)

(a) y₁(t)=te^-1

(b) y₂(t)= t-2

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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