2). ſ y cos(y) sin² (v) dy

Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

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Q: 2. Obtain the general solution to the equation dy dx x sin x y cos y

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Q: 1. S sin’y (2 – 3 cos y)°dy

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Q: Determine the solution to this DE: Cosx dy +(y- cos"x)dn = 0 cos? x Idx = 0

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Q: Solve the given DE: dy ex – 2x cos y ey – x² sin y' - dx

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Q: (2) / 4 cos(x) dx dy 4y 3 (Ъ) r dr de (0)

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Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: Obtain the general solution to the equation dy dr 2+x COS x, y(0) = 2. 5.

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Q: 4x3 — 2х2 — х+5dx А. -2 TT 3 sin t 4 dt cos²t В.

A: Evaluate the integral using the second Fundamental theorem of calculus.…

Q: If y = (3x)sin (2æ) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: y" + 4y = 4 sin(2x)+ 8 cos(2x), y(0) = 0, y' (0) = 1.

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Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: The general solution of the D.E. dy/dx + y cotx = 1 is a. y -cotx + c sin x b. y = -tanx + C CSC X…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 1. Solve (cosxcos y+2x)dx-(sinxsin y+2y)dy=0

A: (cosx cosy + 2x)dx - (sin x siny + 2y)dy = 0 => cosx cosy dx + 2x dx - sin x siny dy - 2y dy = 0…

Q: 2x e²x cos(y)dx + e* sin(y)dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: S S§y²cos(xy)dydx

A: we have given,                 ∫x =0x=1∫y=0y=π4y2cos(xy)dydx After arrangement,…

Q: *10. cos Z = 0.5234 YX _ y 24

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Q: 4: Find aun -2 2y² Sin(xy) dx dy

A: Topic:- application of integration

Q: Take the derivative of this integral.

A: Given

Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: 25 a²y(cos(Tz) +2) dæ dy dz

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Q: What is the first step in eliminating the parameter t from the equationsx= 3 1 sin t and y = cos t -…

A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

Q: Find the complete solution of ey sin x dy cos²x = 0 dx

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Q: If y = (2x² – 3x+4)(e¯* – cos 4.x), then find dy at x = 0 dx

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Q: 4. Find the solution of the equation = e * cos y dy? which tends to zero as x → 0o and has the value…

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Q: トキ 4 Sin Yx cos? dn SinYy

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Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

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Q: cos 2y dy sin y

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Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

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Q: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

Q: 5) Find 业一 dy for y cos(x) sin(x)

A: We have to find the first derivative.

Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x d'y dx? 1-cos4x 6. if y = 1+cos4x du

A: Topic:- derivatives

Q: -T/6 T So Soo S xy sin(yz) dx dz dy.

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Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

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Q: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

Q: 25) 2 sin(y)dx+cos(y)dy 0, y(0) = z/2

A: Q 23 is incomplete as it doesnot contain dy term. and Q 25 is in next step.

Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: 5. Find dt ,y = cos(sin(t – 4))

A: Given function is: y=cossint-4 Derivation of the above function with respect to t. dydt=ddtcossint-4

Q: 3. Find dy dx y= 3 Sin.

A: Find derivative

Q: @2) find to dx 2. y=CoS 2' Sin e

A: To find the dy/dx of the given function

Q: π/3 7. Sp² sin 0 de dp π/6 8. (2-y)dy dx 9. 5/¹¹² x cos y dz dx dy

A: Since you have posted multiple sub parts question in this question which are not interlinked so i…

Q: 1.[* sin'x cos xdx parctan3/2 3secr 2. [ y dy dx J.

A:

Q: x Siny dy + Cosxdx=0

A: Here, we need to solve the following differential equation.                           x sin y dy+cos…

Q: 7+2 sin y -dy = D cos ?y

A: on solving this we get the

Q: 20. e2= cos(z/4) dz

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Q: D. ( [ 3° cos"(5t) dt sin(z)

A: