Problem 1 (Exercise 2.9.1) Find the general solution for t > 0. t²x" + tx' - x=0

Q: if x(t) = tsin(3t) is a particular solution to the equation x" + qx = cost3t, then q = -9. Is that…

A: The given differential equation is: x''+qx= cos t (3t) From the hypothesis, x(t)=t sin (3t) is the…

Q: Show that x(t) = e^t is a solution of tx′′ − (t + 1)x′ + x = 0 for t > 0.and solve the initial…

A: We need to show that x(t) = et is a solution of tx′′ − (t + 1)x′ + x = 0 for t > 0. Note: If x(t)…

Q: 8. x2y' = xy +x²e»/x

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Q: Differentiate with respect to x: x² +2 2 f(x) = O O 4-3x f'(x) = f'(x) = f'(x) = -2x5+ 16x³-2x-7…

A: Given query is to find the derivative.

Q: Solve the IVP

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Q: Let k(x) = (4x2)g(x)h(x). Given the following table of values, find k'(1). %3D -1 0 1 3 h(x) 1 -3 0.…

A: Use the table and chain rule to differentiate the function.

Q: Please solve this: y' = -2xy, y (0) = 2; y (x) = 2e^-x^2

A: Here given that  y' = -2xy, y (0) = 2

Q: What does is mean for two functions f(x) and g(x) to be orthogonal

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Q: g'(2) = g(x) = x + 4

A: dxndx=nxn-1g(x)=x+4x2g(x)=x+4x-2

Q: A ball with mass 1.5 kg is thrown upward with initial velocity 2 m/s from the roof of building 15 m…

A: The mass of the ball is :m=1.5 kg Initial velocity is :The initial height of the ball is :Consider…

Q: If s(0)=−4, s(7)=−5, f(0)=2, and s′(x)=f′(x) on [0,7], determine the value of f(7)? (Do not include…

A: We have to determine the value of f7  given,  s0=-4, s7=-5, f0=2 and s'x=f'x on 0,7 Since, s'x=f'x…

Q: 1.2y" - 5y' - 3y = 0

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Q: 70-5 10 Problem 8: Find f'(x) - 9 f(x) = x 5+1 X ³-1

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: If P(A')= 0.4 and P( A and B)= 0.30, then find P(B|A)?

A: Answer: From the given data, P(A') = 0.4 Since, P(A) + P(A') = 1 P(A) = 1 - P(A') = 1 - 0.4 = 0.6…

Q: Suppose you attempt to use Newton's method to approximate a solution of the equation x² + 5x³+4x² -…

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