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  3. 1.) (10pts) consider the following differential eq

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...

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Advance Math

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 thanone of these types.)

b)Identify the region of the plane where the Chapter 1 Existenceand Uniqueness Theorem guarantees a unique solution exists at aninitial 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

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