A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation y'"(t)+ y(t) = 0. a. Show that y = A sint satisfies the equation for any constant A. b. Show that y = B cos t satisfies the equation for any constant B. c. Show that y = A sint+ B cos t satisfies the equation for any constants A and B. a. Find y'"(t) for y = A sin t. Choose the correct answer below. O A. y"(t) = -A cost O B. y'(t)= A cost O C. y"(t)= -A sin t O D. y"(t) = A sint

Q: ds 4. Evaluate s = In cot 20 in terms of de

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Q: Find the differential of each function.

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Q: h45. Solve for the general solution of y'= sinx + ycotx a. y = (x+ C)sinx b. y = Cxsinx c. y = (x +…

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Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

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Q: Determine the solution of the differential equation dy y cot x = cosx dæ

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Q: 1.) Find dy/dx. Given: x2 +y? = 25 2.) Find dy/dx. Given: x? + y = x³ +y? 3.) Find dy/dx. Given: x +…

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Q: Use the variation of parameters method to solve the following differential equation. y" + y = sec x

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Q: 4 dz = (4x²y + x²)dx + (²x³ — y²)dy = 0

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Q: Use implicit differentiation in finding y'. 1. x²³+y³ =18xy 2. x²y+xy² = 6

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Q: Find the derivative of the following functions. 2. y=e* sec sec x 1. xy=(x-y)+1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given the following differential equation: dy + tan dx a) Solve for the general solution. b) If y(2)…

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Q: 8. Find the differential of each function: (a)y=tan(cos.x) : (b) y=- Answer D

A: 8) a) y= tan(cosx)

Q: 4. Find the derivative of the functions. (2x2-3) a. y = (x247)5 sin x b. y = 1+cosx

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Q: Solve the following first order linear differential equations.   y' + y cosx = sinx cosx

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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.