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: Find the differential of each function.

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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: Find the derivative of the function. y = [x + (x + sin²(x))51³ y' =

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Q: Find a particular solution y, of the given equation using the Method of Undetermined Coefficients.…

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

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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)

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.