dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

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A: We have to find the solution of given differential equation

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: sin (t) -dt 3 (4+ cos (t))?

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Q: dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression…

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Q: d²y Find 2 dx? y = sin 2x+cos² x

A: Using derivatives.

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Q: d Q 3. Prove that tanx dx sec?x. =

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Q: cos r In(sin a)dx

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Q: Using Variation of Parameters 4y''+4=cos-1x

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Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

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Q: T Cos x-sin x Jr x² dx So

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Q: Check by differentiation that y = 2 cos t + 6 sin t is a solution to y"+y= 0 by finding the terms in…

A: Here,  y=2cost+6sint

Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

A: As we know that: The sum rule: f±g'=f'±g' The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1…

Q: dy Find for y = - 7x+5 cos x. dx

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Q: sin x dy Given: y = Compute for dx 1-2 cos x

A: The given function is y=sin x1-2 cos x

Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: Q: Evaluate: 2х -1 cos dx (1+x²

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Q: dy Find for y = - 19x+3 cos x. dx dy

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Q: Using the substitution u = cos(2x), S sin (2x) cos (2x) dx %3D

A: The given integral is ∫sin52xcos32xdx.

Q: dx. (a) [ cosʻ x+4 sin x (i) Evaluate Using the substitution ttanx

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Q: dy Let y=e* sin 3x. Show that 3e-2* cos 3x - 2y. dx -2x d'y = -13y-4- dr Hence show that dx

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Q: 1 – 2xy)y' = yly + sinx] ; when x = 0, у %3D 1 + cosx 1+y²

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Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: dw Use the Chain Rule to find , where w = sin 8x cos 4y, x= dt , and y = t. dw dt (Type an…

A: Given w= sin(8x)cos(4y), x=t/2 , y=t3

Q: The substitution u = tan |converts the integral 2 π/3 1 dx to: n/2 2 +sin x - coS X

A: Given,∫π22π312+sinx-cosx

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: Q2: Evaluate: * Jx* sin(1- x)dx?

A: use substitution method to solve the integral

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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Q: x³ + y³ + 3 x² siny tan z = 5 az dz and əx Find ду

A: Given,          x3+y3+3x2sinytanz=5

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: I sin(z) cos I) COS(2C (x) dx %3D

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Q: dx I [; (1-2x) I= [sin (4x) cos(4x)dx (In(x))3 dx I

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Q: + yž = 1, when x = 0, y = 4 dx cos(x + y), when x = 0,y =" dx

A: The objective is to find the solution of the differential equation.

Q: a) cos(xy)=2y, find y' DI y = cot-1 1+x 1-x

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Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: Q1) Show that: (a) (1+x)° =1+6x :(cosx) = dx = -sinx (e)읊 = E d ( V) = (d) V1+ tan x = 1+;x dx 2 vx

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Hf sin x = A + B cos 2x +C cos 4x, then A = %3D C =

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Q: y = In(cos“ x ) %3D

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Q: Prove that d/dx [cos x] = −sin x.

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Q: a sin a + In v ) da + tan adv = 0 Cos a

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Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

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