Show that both y = sin x and y = cos x satisfy y" = -y.

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A: given equation y' sinπx = y cosπx is solvable by separation of variables

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A: I have stated the used formulas in the solution.

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Q: Solve for the first-order DE: y’+y-y^2(cos2x-sin2x)=0

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A: Given 3x2-y2=t2 and y=tsinθ

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A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

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Q: Find the solution of the equation cos y which tends to zero as x → 0o and has the value cos y whenx=…

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Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

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A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: -(sin(xyz)) = O xô zô y

A: Partial differentiation of the function with respect to x means to differentiate the function only…

Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

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A: Solution is given below:

Q: At what points the curve x = 2a(cos(t))-a(cos(2t)), y = 2 a(sin(t))-a(sin(2t)) has vertical and…

A: Given: The curve equations are shown below. x=2acost-acos2ty=2asint-asin2t Calculation:…

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Q: Show that bothy= sinx and y = cos x satisfy y" = -y

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A: Topic- Derivative

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A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

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A: Given:

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Q: satisfied

A: We will solve the problem.

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A: NOTE: Refresh your page if you can't see any equations. . take x=0 the point on the graph is

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A: Solution

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Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

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Q: Find at the point (5, -1,5) where z is defined implicitly by the equation y°z + x cos z = z sin x.

A: Differentiate both sides partially with respect to y

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A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

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