OSx. ta- x dx OS cot J dxe OSx cot dx -1 S cos' 5ã dx Sx cos dax Ssec x dx O Se dx 10 PSos (dx) dx

Q: cos’x sin x dy + (y cos³x – 1) dx = o %3D

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

Q: 7.x(x² – y² – x) dx – y(x² – y²) dy when x=0, y=0 9. (y – cos?x) dx + cosx dy = 0

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Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: dy 4. x sin y = cosy, (x cot y + 1) = -1 dx

A: Given. xsiny=cosy We have to derive the differential equation dydxxcoty+1=-1 from the given…

Q: dy ez? = 0 5. x+2xy2 + y- dx (Hint: separable)

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Q: dy = Cos (x +y + 1) 15. dx

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Q: Fiud ť amalytic Ť Ref = (t+y) · cos(2=y").

A: The objective here is to find f analytic. Ref=x+ycosx2−y2

Q: Question 16 dy Find dx of 2/x + Vỹ = 1. (A y - 2 Vxy B 2 y 2 x y

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Q: 1. cos?x sin x dy + (y cos³x – 1) dx = 0

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Q: (1* -1) (4 – x² )dx Je* . sin e* dx Stan(3x +5) dx * cot(Inx) dx sinx + cosx dx cosx dx 1+ cosx…

A: (1) ∫x2-14-x2du =∫4x2-4-x4+x2du= ∫-x4+5x2-4  du=-x55+5x33-4x+e (2) ∫ex.sinex du Here, ex=u…

Q: 3.fe²x cos 3x dx

A: The given integral is ∫e2xcos 3xdx Integrate by parts  where first function is e2x and second…

Q: (a) dx [(x – 1)(x + 7)] (r + d^)u] (a) (c) do [sec(0*)] d (d) [arctan(2x)] dx

A: Here the objective is to evaluate the following:

Q: dy/dx= 4 cos 4x

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Q: The dy/dx for y=-4x+7 cos x d/dx (-4x+7 cos x )=

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Q: (x* +y' )dx+(2xy+ cos y)dy

A: Follow the procedure given below.

Q: dy - y cos x dx = y ln [yedk COS x]

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Q: dy - y In(ye cos *)dx = y cos x dx COS X

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Q: i y = tan-1(x)+ tan-1() dy + 10 dx

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Q: y dx + cos x dy = cos?x dx %3D

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Q: dy dx 2 cos y 3 Csc x

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Q: dy Find dx -1(In 8x*) y= tan %3D dy %3D dx

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Q: dy 1-5e + y cot x 5e", with y(z/2) =-4. Cos 7) %3D Ans.: y = dx sin x

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Q: (y? cos x – 3x?y – 2x) dx + (2y sin x- x'+ In y) dy = o

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Q: Find dy dx 1. 2 y = coth(esinx) tan-1(oooh x3)

A: As per bartleby guidelines we only give first question answers.

Q: dy (2x sin h -+3y cos h -) dx Зх cos h - 2 tan h 3 + ||

A: According to the trigonometric hyperbolic formula: tanh(x)=sinh(x)cosh(x)        ...(i) Distributive…

Q: h) (3X 9'+4y)dx + (3 X'9 +2x) dj = 0 I) sin X dy dx Sin 2X -y cos X

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Q: Find dy/dx of y=sin-!x+cos-4 dy/dx is Blank 1. Blank 1 Add your answer

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Q: dy, ycosx+ sin y + y_ o Solve dx %3D sin x + x cos y + x

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Q: dy y%3D 1+sinx cos x lb) find dx

A: Given

Q: y²dy e2x а. dx У (0) %3D 1 ex b. 8 cos? y dx + csc² x dy = 0, %3D y 12 4

A: Part(a) We have  y2dydx=e2x+1ex, with initial condition y0=1 This can be written as: y2dy=e2x+1exdx

Q: i. S(e** cos(2x)) dx

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Q: * = cos(x + y), when x = 0,y = = %3D dx

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Q: Find dy/dx and d²y/dx². x = cos 2t, y = 3sin t, 0 <t < n dy dx d?y II II

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Q: y = In (tan -1 (8x°)) dy dx II

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Q: (y? cos x – sin x)dx + (2y sin x + 2)dy = 0 (Exact)

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Q: sin?y dx + cos²x dy = 0 ; y (÷) =÷

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Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

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Q: COS X %3D dx dx COS 9 212

A: ddxdydx=ddx-cosxcosy

Q: Find dy dx the function y=2 sin 3X cos 2X

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Q: 4x Cos x dx b.

A: Given :

Q: 20.1 please provide all necessary solutions and explanations.

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Q: dx dt 2w3 d. dw Sin (x)-InIxldx

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Q: dy A-Find of the following: dx tan(5u) (1 + 2u)³ , u x. sin(x).csc(x) y = U = e4u

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Q: . (бх + у?)dx + у(2х — Зу)dy %3D 0 . (2ху — tan y) dx + (x? — xsec'y)dy -о

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Q: X cos (3x) dx,

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Q: d Cvaluate dx cos (r² + 1) dt

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Q: dy = 4 cos 4x dx

A: The given differential equation is dydx=4cos4x. We can solve this differential equation using…

Q: dy dx 2. 2X for y = cos (Inx + e) %3D

A: ddx(Cos(x)) = -sin(x)ddxex =exddx(log(x)) =1xddxxn=nxn-1Chain ruleddxf(f(x)) =f'(f'(x)) Here , In…