do the functions, ex/² and xex/2 form a fundamental set of solutions of the differential equation, 4y" - 4y² + y = 0 ² if on which indicate the interval the solution is valid yes,

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A: Kindly refer to Step 2 for the solution.

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Q: K Consider the function f(x)=sin(x7). a. Differentiate the Taylor series afout 0 for f(x). b.…

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Q: 3. Find the local extrema of the given function =(x,y)=18y+x³+y2²- 6xy - 39x -3

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Q: 2. Using reduction of order find a general solution of x²y" + xy' - 4y = 0, y₁ = x².

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Q: 1. Which of the following differential equations is linear? a. y' + y² = c. yy' + 5y = cos x = X b.…

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Q: 5. Find a formula to estimate the first derivative f'(x) by the function values f(x), f(a+h) and…

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Q: d) f(x) = (x²+1)/(x²+2)

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Q: y" + (x-7)y = 0

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