Use the variation of parameter method to find a particular solution d²y * + 4y = sec? (2t) Yp of (You may use f sec tdt = In sect + tan t| = C)

Q: Q3) find the derivative of each function: 1) y=x?sin*2x + x cos-3x 2) y? = (sin2x)* + (cos2x)* + 2xy…

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Q: A bullet fired from a gun follows the trajectory x = at, y = bt – 16t2 (a, b > 0) Show that the…

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Q: Differentiate: y = cot(xcsca) = cot x (xcsca - 1) csc (zcsca) Oy = cot x (xcscx +1) csc (xcscx) =…

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Q: Question: Find the derivative. tan 3x y = (x + 7)ª Select one: 3 (x + 7) sec?r (3x) – 4 tan (3x) y'…

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Q: 41n <ys 28 31r x = sec* (7t) – 1dt, | 21 41x 28

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Q: y"+y = tant, - < t <Hint: use variation of constants me

A: Given differential equation Lets first convert it into second order differential equation and then…

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: 7/12 16.r(sec 4.r) dr =?

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Q: Find the indicated derivative dy/dx 3.) x+xy+y=1

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

A: Solution

Q: 2.x²y+ 3xy? = 2x + 55

A: We will find the value of dy/dx and the equation of the tangent line at point (5,1) in the following…

Q: Q9// find the general solution (sec'x + (cotx)y)dx + (Insinx)dy = 0

A: Using the basic properties of trigonometry and expanding the expression we can find the solution to…

Q: Use variation of parameters to find the general solution of x' = Ax + f where 433 A =e¹[¹] f = et

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Q: Determine the equation of the line that is tangent to y = 2 tan x, where x = 4. O-4x + y - (2-) = 0…

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Q: y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: Find f’

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Q: If function a solution of differiential equation? Shoe work  y=sqrtx; xy'-y=0 y=x^3; x^2y" -6y=0

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Q: @ Find an equation of the tangent line to the curv@ x² + y² + xy = 16 at the point (0, 2). 4 b) Find…

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Q: dt dp dt о dp dt о dp dt S 3t tan 3t = 3sec t tan 3t 3sec3t tan 3t = 3 sec 3t

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Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

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.