1. y = Ax² + Bex 2. y = C₁ ex cos3x + C₂ ex sin3x 3. y C₁e* + C₂e²x + x 4. Iny = C₁e* + С₂е¯* 5. x = cos(at + a) Note: Eliminate ß and a, wo is a parameter not to be eliminated, then differentiate with respect to t.

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Q: 12. Solve: v v&vv 1 52-* 125 a) log, 46 656 b) log,8 = log, 256

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Q: Explain briefly the classifications of the Differential Equations?

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Q: What are modeled with differential equations?

A: Here we define the differential equations.

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Q: Describe the impact of duality on the understanding and analysis of linear differential equations

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Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.

Q: Give your own example of a first order linear differential equation and solve it. Explain the…

A: An example of the first order linear differential equation is given below.