Suppose we are given y1(x) and y2(x) (with y1 # y2), which are two different solutions of a nonhomogeneous equation y" + p(x)y' + q(x)y = g(x) (1) In three steps, describe how to write down the general solution of (1): Step 1: Step 2: Step 3:

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A: we have given particular solution of the given differential equation.

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A: Given: 2y3-y2-2y1+y=4x3-2xe-3x+5sin4x Initial conditions: y0=1, y'0=-2, y''0=3

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A: To solve the given Homogenous IVP using the method of undetermined coefficients.

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A: We will find out the required solution.

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A: We will solve the given differential equation.

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Q: 2. Find a particular solution of the nonhomogeneous equation a. y" - 2y' + 5y = 6e3x

A: As per our guideline we can solve maximum one question ,you can repost other in next turn

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A: The solution is given in the next steps.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.