True or False 1.  The functions cos left parenthesis 3 x right parenthesisand 2 sin left parenthesis 3 x right parenthesis are linearly independent. 2.  The D.E. 3 left parenthesis d squared y right parenthesis divided by left parenthesis d x squared right parenthesis plus x y equals c o s left parenthesis 3 x right parenthesisis a second order, homogeneous. 3.  The purpose of doing Wronskian is to determine if a set of solutions is linearly independent. 4. Laplace Transforms changes a differential equation into another one with a different variable so it can be solved algebraically. 5. 1st Ordered D.E. can be considered as a Higher Order Differential Equation.

Q: Use the Linearization Theorem to classify the equilibrium point y = 0

A: To Linearization  dydt=ycos(4πey) and classify the equilibrium point y = 0.

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A: Since F is not conservative so we can not solve the part b and c.

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A: Here corner points are , (0,0), (0,3),(3,0),(2,2) At (2,2) we have optimal solution.

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Q: Let k and a be arbitrary integers. Prove that a is even if and only if ka is even.

A: SEE BELOW FOR TGE COMPLETE SOLUTION

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Q: 02. The general solution of y" + 6y' +10y = 39 cos(t) is -3 A. y=e-³t [C₁ cos(t) + C, sin(t)] + 2t…

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Q: a. How large is the property in​ acres? b. If the property is selling for $450,000​, what is the…

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A: Solve the differential equations

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Q: #18

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Q: 33. Compute each of these double sums. 2 3 a) Σ Σ(+j) i=1j=1 3 2 Σ Σi i=1j=0 c) b) d) 23 Σ Σ (2i +…

A: we have to solve the given double sums.

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A: Q3 asked and answered.

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