Q.3.a).lf « & ß are real numbers, ß # 0 then the function y, = e" cos ßx and y, = etr sin ßx are inearly independent. Also determine its differential equation.

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Q: #1 y= x³ + 4x − 15 at x = 0

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A: The given function is - y = x(x-5)2y' = -x+5(x-5)3y'' = 2x+20(x-5)4

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Q: y = x³ + 4x - 15 at x = 0

A: Formulas to be used: 1) Newton's Forward Difference Formula The formula for the forward difference…

Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

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A: As per guideline we have to solve three subparts

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.