A dynamic system is represented by the following differential equation. y" - y' - 2 sin y = u(t), u(t) = sin3t Where u(t) is the input signal and y(t) is the output with the initial conditions y (0) = 0 and y' (0) = -1. Linearize the differential equation above at equilibrium point at y = 0, u = 0, and solve using Laplace Transform method only.

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A: We will solve the pde using lagrange's auxiliary equations.

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A: See the attachment

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Q: Solve the partial differential equation of Lagrange's form  xy2p-y3q=-axz.

A: Given equation is  xy2p-y3q=-axz            (i) Lagrange auxiliary equation is  dxxy2=dy-y3=dz-axz…

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Q: 5. A differential equation is if it can be written in the form f(y)d(y) = g(x)d(x)-

A: A differential equation is ORDINARY if it can be  Written in the form f(y)dy = g(x) dx .

Q: The differential equation 4y"- siny y' + 3y = O is a linear equation. :Select one True False

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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.

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Q: Solve the partial differential equation of Lagrange's form  xy2p-y3q=-axz.

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