Consider the ODE and let Find the value(s) of a for which y(x) is a solution of the ODE. Hint: Substitute y(x) into the ODE. a = y(x) = dx = 3-3x²y²-y where x > 0 tanh(ax+7) X If there is more than one value, then enter them separated by commas, for example -2,1 If there is no such a, then enter NONE where a ER is a constant.

Q: Find a and d for the function f(x) = a cos(x) + d such that the graph of f matches the figure. a = d…

A: From the given graph, we see       f(0) = -10       f(π) = -2

Q: It can be shown that y₁ = x³ is a solution of the ODE: x²y” — xy' − 3y=0. Use the method of…

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Q: The function f(æ) = tanh I> 0 is equivalent to which of the following functions Select one: 2x -1 a.…

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Q: Let n be a positive integer. Define the function fn(z) by dn dzn Find the value of fn(-1+i).…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: f(x) A B = arcsin x, then lim 1/1/12 0 ㅠ 6 f(x)−ƒ( ² ) X→ X- 1|2 is

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Q: Determine if each statement is true or false. If a statement is false briefly explain why it is not…

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Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…

Q: Let h(x) = tan(2x + 7). Then h' (3) is and h'' (3) is

A: Given query is to find indicated derivative

Q: a. f(t) = cos(2t). Find F(s) b. g(t) = e²t sin(3t). Find G(s) c. H(s) = 3s +1 s² - 2s + 5* Find h(t)

A: We have to find the Laplace transform and inverse Laplace transform.

Q: Determine algebraically whether the function or neither. f(x) = COS sin z +3x is even, odd,

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