Problems 3,4, and 6 2. Classify each of equations given below as directly-integrable, separable, linear first-order, linear substitutive, homogeneous, Bernoulli, or none of them. Find the solu-tions to those equations.dy(1) x= 2y – 6x3dy(2) 4x2 -x2y² +0.dx(3) x2.dyVT = 3dxdy(4)= y? – 2ry+a?dxdy= 0(5) 3ry3-y+x-dxdy(6)dxry-3x(7) 2 cos(x)dy= sin(x)d.xdy(8)dxtan ()山一

Answered: dx dy (3) x2. Va = 3 x%3D dx

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Homework 10: Question 1
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Problem. 13: Compute the product. 2 -35 2 -2 4 1 -1 4 -1 -3 -41 ? ?
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Problem 5.4 (Grade a "Proof"). Study the following claim as well as the "proof": Claim. For all n e N, 3| (n³ +44n). “Proof". When n = 1, n³ +44n = 45 is divisible by 3. When n = 2, n³ +44n = 96 is divisible by 3. When n = 3, n³ + 44n = 159 is divisible by 3. When n = 100, n3 + 44n = 1004400 is divisible by 3. Thus 3 | (n³ +44n) for all n e N. %3D Complete the following questions concerning the above claim and "proof": (1) Determine whether the "proof" is rigorous. Identify the issues in the "proof", if any. (2) Determine whether the claim is true or false. Justify the answer in part (3). (3) If the the claim is true and the “proof" is not rigorous, then provide a correct and rigorous proof. If the claim is false, give a concrete counterexample. Hint. Complete the parts as instructed. If the claim is false, then (obviously) there is no way the "proof" could be correct.
21). can someone solve this and explain with details please

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