Consider the first-order differential equation for y(x): dy = y tan x + sin x . dx du find a differential equation for u(x) in terms of u(x), dx Let u(x) = y(x) cos x. By calculating du and trigonometric functions of x only. By solving the equation you have found, find the dx general solution for y(x) and the particular solution when y(0) = = 1.

Q: Solve d²y dx² - cot x dy-sin² x.y = cos x - cos³ x. 2 dx

A:

Q: Find the differential of each function.

A:

Q: Find the differential of the function. z = e-5x cos(9xt) dz = dx + dt Need Help? Watch It

A:

Q: (a) Find the derivative of the following functions (i) y = a² sin“ x +æ cos-2 x. (ii) y = e(+v#+x²),

A:

Q: Find the derivative of the function. y = sin−1(3x + 1)

A: Given data:     The given function is: y=sin-1(3x+1).   The given function can be expressed as,…

Q: 0·1 sin(x)dx X

A: Use the nonelementary integral:

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

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

Q: dy of the function dæ Find the derivative x* In 3y = y sin 3x + et.

A:

Q: sin(y)dx + cos(y)dy = 0 by exact

A:

Q: x(t) = 2 cos(200pi(t)), t ≥ 0 . Write in standard form.

A: see below the answer

Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

A:

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

A:

Q: x2 + a Consider the function Find the value of the constant a so that y' (1) = 0.64

A:

Q: y+y=sin(x), where y(x) = 1.

A:

Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and da Find the differential dy when x = 3…

A:

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

A: 8) a) y= tan(cosx)

Q: Find y' for the function as shows below.   cos(xy)=x6-y

A:

Q: Find the differential of the function. P = 99 - 293/2 dp = X

A:

Q: Find the differential dy of the function y = 4x²-x+ 3 Select one: O a. (8x-1)dx O b. (x²-x² + 3x) dx…

A: Solve for the differentiation

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.