The general solution of the differential d’y + y = f (x), xe (-0, 0), where dx? equation f is a continuous, real-valued function on (-00, 0), is (where A, B, C and k are arbitrary constants) (a) y(x) = Acos x+Bsinx+ [f (t) sin(x-t) dt (b) y(x) = cos (x+k)+ (t)s (x-t) dt %3D (c) y(x) = Acos x +B sin x + [ f (x-t)sint dt (d) y(x) = A cos x+Bsin x + | f (x+t)cost dt %3D

Q: sin(t) dt , 1-4x 1+ t2 4 If f(x) then f' (x) =

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Q: 2. Let F(x) = x s sin (t2) dt. Find F'(x). (a) sin (x²) dx (b) sin (x²) (c) sin (x²) + C (d) 2x sin…

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Q: sin(2t +) dt eu-3 %3D 64

A: Let, I =∫0∞sin2t+π2e2t-3dtApply integration by part ,Ist function = cos(2t) , since sin(π/2+x) =…

Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

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Q: The complementary function of the differential equation d²y dx² 2 + 3x +y= dy dx 1 is (1-x)²

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Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

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Q: Find the differential of each function. (a) y = 2 + 55 dy (5s + 2)² (b) y = eu cos(u) 1. dy =…

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Q: Calculate the derivative of t2 -k 3 - t F(t) = cos(t) i + 3e2t+2j + |

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Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

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Q: Write the equation „dr te +x dt dr in the form of +p(t)x=q(t). Then identify p(t) and q(t). dt…

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Q: 1. Use the basic differential properties shown in section 3-5 to find each indicated derivative. (A)…

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: Solve the ODE with differentials operator (D²+4)y= cos(2x) + cos (4x)

A: Linear ordinary differential equation

Q: What is the partial derivative that verifies (cosx + Iny) dx + (x/y+e') dy as an exact differential…

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Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).

Q: (b) x = dx dt 1 sin7 (t³)

A: Given:- x=1sin7t3

Q: -Jo + sin(tº )]dt, find f(4). f(x) = dt, where g(x) = (1

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Q: Consider the function. y = (2x² + 1)³ (a) Decompose the function in the form y = f(u) and u = g(x).…

A: We have to find given decomposition and derivative of y.

Q: Find the differential of each function. (a) y = x2 sin(4x)

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