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Q: Solve y" - by'tlly - Slt-1), ylo)= 1, y'lo)=0 ylo) = |

A: The given function is  y''-6y'+11y=δ(t-1) The initial conditions are, y(0)=1, y'(0)=0 We find the…

Q: arcsin(4x)/arctan(5x)...

A: Using L'Hospital's rule to evaluate this limit,we know that,if  is of the intermediate form or…

Q: (f) / sec“ y dy. tan5

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Q: -5 sinx dx I = =? ecosx +3e-cosx ) +c COSX a) arctan 3 cosx b) arctan + C

A: To find ∫-5sinxecosx+3e-cosxdx

Q: 2 sec wdw a) 1

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Q: f(x)=x+5 glx)=x -1

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Q: (7) 3x-7>11 ans./ (-co, -4/3) u (6, co)

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Se-*sin 4x dx

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Q: Find Lte " sin 41]. -2r

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Q: dz -i|=1 (22+i) "[( -- 1)]

A: We need to evaluate ∮z-i=1dzz2+i

Q: 2. Is trigonometric substitution needed to evaluate /9 - x² dx?

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Q: fostp Ex=(Xzy)=-3:52-25)

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Q: and flo)=-9

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Q: Se** sin (4x) dx

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Q: Find sin a. (-/5 ,2) [ ?] 1

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Q: A particular solution of y" + y =sinx + xcosx a. x?sinx - 2xcosx) 4 b. (x?sinx – xcosx) 4 c. (x?sinx…

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Q: Differentiate y = 5 sin(2x-4). O a) dx = = -5 sin(2x-4) о O b) ad ax O c) = 5 cos(2x-4) = -10 sin(2x…

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Q: fcos:fin x - sin' x )dr.

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Q: sinh x 20. 1x1-3 A) 2. B)-2. D) 0.

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Q: 5)find y y= Inl-decx +tanx)

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Q: 2) sec tan 4

A: Solution: The objective is to find the required value

Q: Y"+y=secxtanx

A: Given, y'' + y = secx tanx This is a second order linear, non-homogeneous ODE. We can write the…

Q: dy - (1+x)у -ху? .2 1.) х- dx

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Q: 15 S(+ 15e15x – 15x-1 + 15n) dx. x-14

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Q: Differentiate, hcx) = In (x-Vr

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Q: tan' sec? 그dr 26. 28. 7 dr - 10

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Q: f'«) ių faa) = arcsin Ve^

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Q: 4) S tanx dx cosxv1+secx 5) S(1- u)Vūdu

A: (4)  First we integrate this ∫tanxcosx1+secxdx

Q: St) = r°+x}

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Q: tan³ r sec' rdr

A: The given integral is ∫0π4tan3x sec4x dx. Let u=sec x. Then du=sec x tan x. Then, the lower limit…

Q: Solve y"-2y't3y =eľ tang

A: Use the formulas of solving second order differential equations. A solution is a sum of…

Q: 41 Cx) = 7x² +Y all fla) = bl flath= a fla la) - thl-f

A: Given function is:                                 (1) a) To evaluate Substitute  in equation (1)