show that Pg(x) =1 (63x' -4 (63x-7ox+15x) 8. Legendre equation when is. equal to 5. fies the farameter

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Q: How would I approach this problem algebraically, and analytically? I have attached a photo.

A: To find:

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A: By using integration formula, we calculate the given integral.

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Q: 30. 5e dx 31. Зи du - 1 33. x² dx 35. (x+5)* 37. xp (3 In z + 2)4 39, -dz

A: We will solve the integration.

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Q: II. Solve th following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 %3D -

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Q: dy Exc:" of y = tanh (x5 – 5x)² --

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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.