Question 5 Solve x4y (4) + 6x³y (3) + 25x2y + 19xy' + 81y=0 where x > 0 c cos (31nx) + c sin (31nx) + c cos(x) Inx+c_sin (x) Inx t c cos (3lnx) +c sin (3lnx) +c cos (3lnx) Inx+c sin (3/nx) Inx 4 c cos (3lnx) +csin (31nx) +c cos (3lnx) +c_sin (3/nx) c cos (3lnx) +c_sin (3x)+c cos(x) Inx+c sin (3lnx) Inx

Q: fr cos xdx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1 -dx = /8-(2x+5)² o įsin- (2*) 2x+5 + c V8 2x+5 sin-1 + c 8, tan- ( V8 2x+5 + c o ţtan" (2*5 ) + c…

A:

Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

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A:

Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

A: Given

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A: (1).   The given trigonometric equation is:4sec(2θ)-5=3

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

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A: Here we have to evaluate I=∫(x-3)sin-1lnx+cos-1lnxdx

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A: Can solve the given function by using double angle formula

Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

A: First, we need to identify the type of integral we are dealing with. The first integral is a product…

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A: Hence proved

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: Solve x 2x 2x 2π cos - ( 2² -1) + sin ~¹ ( 24₁ ) + tan - ( ²²₁ ) = ² COS 2 +1 x +1 3 -

A:

Q: | -3x cos 4x dx A) - 16 3 cos 48 -x sin 4x + C 3 3 3 B) cos 4x -x sin 3x +C 16 3 cos 4x - 16 3 C) -…

A: To evaluate the given intgral.

Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

A:

Q: cscx−sinx cos²x CSC X =

A: We need to prove that cscx-sinxcscx=cos2x

Q: Find the solution. (403+12D²+13D+10)y = 0. @ y=c,e+e>(c,cosx + c sinx) +c,sinx) -3x y =…

A:

Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

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Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x) SinZx [cos(2x) – 1]+ 8 * + C + 12 sin(3x)cos(3x),…

A:

Q: Differentiate: x¹0 cos(x)

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Q: Ísin^8 (3z) cos^5 (3z) dz * O 1/27 cos^9 (3z) - 2/33 cos^11 (3z) + 1/39 cos^13 (3z) + C O 1/27 sin^9…

A: Given integral I=∫ sin8(3z) cos5(3z)  dz

Q: If 4 f(x) = %3D 1+ sin x then 4 cos x f'(x) = (1 + sin x)²

A:

Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) , sin(2x) + + C 12 8 8. 4 sin(6x) sin(2 x),…

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Q: +3x2, (V)² = sin³(cos³(*3**» dy b. Find dx %3D

A:

Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…