(a) y' + 2y = 26 sin 3t, y(0) = 3. %3D (b) y" + 3y' + 2y = 6e-t, y(0) = 1, y(0) = 2 (c) y" +9y = g(t), y(0) = 1, y'(0) = 3, g(t) = S 6, 0

Q: Find y' if y= cos (X-1) X-1

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Q: y' + y tan x sin x cos With y(4) = 0

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Q: y = (c1 + c2e2= + c3e¯® + C3e¯ cos(2x) + c4eª sin(2x))

A:

Q: 2 (x² + 1)y' = 2x cos² (y) with y(0) = 7. 4

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Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: y" (t) - y(t) = 4 cos(t) ;y(0) +0 , y'(0)=1.

A: The objective of the question is to solve the given second order differential equation with the…

Q: Which one of these equations is not separable? (1) xy' = y ln |x| (2) y' = In y' (3) = x + sin(x)…

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Q: x cos'(y)dx + tan y dy = 0, y(4) = 7 2. X COS

A:

Q: If f is a differentiable function and y = cos(f(x3)), what is 2 when x = 2? (A) – sin(f'(8)) (B) –12…

A: Here to find the required derivative we have to apply the chain rule of differenciation.

Q: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

A: Topic :- Derivative

Q: Fihd f if f"(±) = sin(z), f(0) = -1, f'(0) = -1, f"(0) = -4. %3D f(z) =| D

A: Given: f'''(x)=sin(x),  f(0)=-1,  f'(0)=-1,  f"(0)=-4

Q: y" – y' – 2y = sin 3t y(0) = 1 and y'(0) = -1

A:

Q: 3 Parameterize y(x) = +1 using x = t sin x Ans=

A: The answer is: y(t) = (-3/sin(-3/sinx) + 1)) + 1Explanation:To answer this question, you just have…

Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: y'' - 15y' + 60y = e^x cos(16x

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Q: Y= (X+SinCe)? Find a(x) and fG) y=foq> (x) 3. (fog)'= %3D X+Sin(x) gcx) at y ' ( x)) X+ Sin (x. %3D…

A: (fog)(x)= f(g(x)) So, f is the outer function and g(x) is the inner function.

Q: (1+x)y' + y = cosx; y(0) = 1

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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: -x* ]y" – x y' + y = - x cos x ; y(0) =0 ;y'(0)=1 COS X

A: Given that, (1-x2)y''-xy'+y=-xcosx,y(0)=0,y'(0)=1 Take y=a0+a1x+a2x2+a3x3+a4x4+a5x5+... Take the…

Q: (b) y"(x) + y(x) = 3x² - 4sin x, y(0) = 0, y'(0) = 1

A: The given differential equation is

Q: (a) (b) y' = 2y + t²e²t ty' + 2y = sin(t)

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Q: If f(x)=√x+3, g(x)=x², then (fog)(x) = The differential of the function f(x)=tan(cos.x) is_ The…

A: We know that derivative of d(cosx)/dx = -sinx. And d(tanx)/dx = sec2x. And derivatives power rule is…

Q: If f(x, y) = x² tan¯' (4) – y² tan¬1 (4) , then fy(0,0) = 1 -2 2 -1

A: Given: f(x,y)=x2tan-1yx-y2tan-1xy To evaluate: fxy(0,0) We know that fx(x,y) is partial derivative…

Q: (b) y"(x) + y(x) = 3x² - 4 sin x, y(0) = 0, y'(0) = 1

A:

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.