Find the general solution of y' =y sec x. A. y = C (secx+ tan x) B. y= C (sec x – tan x) C. y = C (sec x tan x) D. y = C (sec 2x + tan x)

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: y" – 9y = t° – t e + sin(3t)

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Q: y" + y = sec x tan x

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Q: S(sec a tan x 5æ4)dx tan x + x +c - sec x + x' + c sec x – x5 + c sec x + x +c sec x – x + c

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Q: Find y SX a) y = 3 sin (x² + 5x - 3) y' = c) y = sin" (6x) y'= b) xE5X+2 d) y = In (2x) Y₁ = Y y' =

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Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: (cos y+ ycosx)dx + (sin x –xsin y)dy = o

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Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

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Q: find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0,…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

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: IV. Implicit differentiation 1. xy + y? = 1, find y? 2. x²y – xy? + x² + y² = 0, find y' 3. x? – xy…

A: Given: 1.xy+y2=1 , 2. x2y-xy2+x2+y2=0 3. x2-xy+y2=3 4. x3y+xy2=3 and x=1

Q: 1. Find y' of tan(x²y*) = 3x + y² Answer: y': 3-2xy* sec²(x²y*) 4x² y3 sec2 (x2y4)-2y

A: We will solve the problem

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: e* tan (e*) dx sec2 (e*) – 7

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Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 47. Show that y = x³ + 3x + 1 satisfies y"" + xy" - 2y = 0.

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Q: 4 (a² - y²)² 4. g(x) = (3x² + 4x - 5)5 3. 2 =

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Q: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

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Q: Find the derivatives of the following: 1.) x* + 2y = 6x 2.) f(x) = (tan 5x) (x + 2)²

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Q: f(x.y) = xtan(). =tan( ес

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Q: Solve dy dx Option 1 - y tan x = -y² secx 1- y = sec² x + tan x + C 3- y = secx + tan² x + C 2 y-¹…

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Q: X₁. (x₁, Yr) (x', y') 0 (x, y) X x' = x + (x-x, )cos-(y-y,)sin y' = y, + (x-x) sin 0+(y-y,) cos P' =…

A: Solution:

Q: Q2) Find the general solution for this equatio- y" + (tanx-2cotx)y' + (2cot²x)y = 0 If you know that…

A: Given differential equation It has one solution Lets use method of reduction of order.Assume the…

Q: Y(6) = cot(5s)- 3 tan s - csc (5s)- 3 sec' s s:y (s) |

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Q: sinxcos ydx + cos²xdy=0

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Q: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

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Q: Ir x²y" + xy' + (x? - +>v =0 x >0 || | 1 - 2 sinx ,V1=X the following equations satisfied by v and y…

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Q: Q1) Find the first derivative of the following equations: y = x'V

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Q: y+y=sec²x-tan x Find the solution y(x) X

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