Consider the equation ¨x = ax. If a = 0, than the solution of this equation is x(t) = C + Dt where C and D are the integration constants. Find the solution of the equation x¨ = ax and show that in the limit a → 0 it reduces to x(t) = C + Dt.

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A: Let .To find the following:

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Q: дх 5 + 2¹(1² 1 -)dt

A: To find the derivative

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A: The integrating factor for given differential equation is

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A: Solution

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A: details steps are given in step 2

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A: follow next step

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Q: 2: Find the orthogonal trajectories of xy=C.

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A: Let . To find the following.

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A: NOTE: Refresh your page if you can't see any equations. .

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A: Find the eigenvalues of A.

Q: The

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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.