1. Which of the following functions is a solution to the IVP yy"= y1, y(1) = 0, y(1)=1? (a) y = e²/2 (cos √3x + sin √3x) (b) y = -(e²-¹ - e¹-²) (c) y = x (d) y = x lnx ✓ (e) y = (x + lnx) + ln(x + Inx)

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: 3. Find f. (a) f"(x) = x + 12x² %3D

A:

Q: Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

Q: Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

A:

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(71/2) = 0 %3D %3D

A:

Q: Incorrectly, we usually say that when we multiply any number by ten we “add” a zero to the number.…

A: a) Jushua is wrong because the correct answer is 10×1.3=13 b) If a whole number is multiplied by 10…

Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: 3. Find g'(x) if g(x) = sin³(4x) %3D A. cos (4x) B. 3 sin?(4x) cos(4x) c. 12 sin (4x) cos(4x) D. 4…

A:

Q: 2. 1 Evaluate the definite integrals below. Use u-substitution when appropriate. 4 5 3el/x (a) (b) |…

A:

Q: If y = -cos(2t), then y(5)= ?

A:

Q: Given a rate of 175 pesos per hour, how many hours should you work to earn 35,962.50 pesos

A: If ∆x is the amount earned in time ∆t, then the equation for the rate of the amount earned per unit…

Q: Q3 Check the symmetry and graph the curve in polar form if 0 = 0 and equal 1/6 to 1/2 at increments…

A:

Q: 2. Solve 3 y'(z) + y(x) = y²(z) (cosz - sinx)

A:

Q: Solve: y" + 2y' + 2y = 2 sin(x) +3 cos(2x)

A:

Q: s¯¹(x + 1) − √√14 − 3x², find ƒ¹(x). If f(x) = 3x cos

A:

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: dy cos?x = -(tan x)y ;y(0) = -1 b) Solve %3D dx

A: Given that: dydx-cos2x=-(tanx)y; y(0)=-1

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: Solve y' = cos(2x + y – 5) – 2. = COS

A: The solution is given as

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

A:

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

A:

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

A:

Q: Find f. f "(x) = 5 + cos(x), f(0) = –1, f(9/2) = 0 f(x) : %D

A:

Q: // (cos (a? + y³)dA where D: {(x, y) | 4 < x² + y² < 49} Find

A:

Q: If y(t) is the general solution for the equation: y' + y = sin(t), y(pi/2) = 0 Then, y(0) = ? a)…

A: Consider the differential equation  y'+y=sint,           yπ2 = 0

Q: Determine f,(x); f(x) = cos(2x³ +n²)

A: