а. 2хеУ dx + (x?еУ + сos y) dy — 0 b. [sin(xy) + ху сos(ху) + 2x] dх + [x? сos(ху) + 2y] dy

Q: Evaluate [[ sin(y²)dydx where 2: 0<y<1, 0<x<y°. 0 x b) a-cos¢x)) (1 a) 1-cos(x) 1 - cos(1) c) 2 d)…

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Q: 5- for y = (x² + 1)5 dx a)10(x² + 1)5 b) 10x(x² + 1)* c) (x² + 1)* 6- Sin 2x is equal to: a) sin x…

A: Answer of the above questions are

Q: 18) e2x = sin(x + 3y)

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Q: 28+1 b:If y =-1 prove that. 1- 2y dx

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

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Q: Obtain the particular solution for the following set of differential equa dy = (4x2 + 7xy +2y²)dx;…

A: Given that: x2dy=(4x2+7xy+2y2)dx        and when x=2, y=0

Q: 5. S 11 sin ( 4x – 6y) cos ( 6x – 4y) dy - -

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Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

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Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: 2. Evaluate a. [x'(2x° +5)' dx b. dx V1-7x c. [cos 3xsin 3xdr d. sin* 6x cos 6xdx e. [t* cos(2r'…

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Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: 1- d/dz [cosz] = -sin z

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Q: 1. Find the differential of w = x cos y – y sin x.

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Q: 8)find dy/dt for y=cos^2(3#t-1) # is actually pie or 3.14 etc I just don’t have the symbol on my…

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Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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Q: 21. If y=(x* +sin x)", then dy dx (A) 6(x*+sinx) (4x-cos.x) (B) 6(x*+sinx) (4x' +cosx) (C)…

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Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

A: Given ∫x2x2+34dx

Q: 22 3x'y = 2ty- 3). 23 (2y cos x + sin* x) dx sin x dy; when x Ans. y= cty- 3) exp (x n, y = 1. %3D…

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Q: 一3十 Sin zt dt

A: We have to use first shifting property and Laplace transform of integration property to Laplace…

Q: 5) S V2 + sin 3t · cos 3t dt

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Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

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Q: 9-x 4. Evaluate ſ, S sin(x² + y²) dy dx

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Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = i

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Q: 18) * x-sin 2x ; find y" y y" cos 2x y = 7 %3D Option 3 O Option 1 y" sin 2x

A: First we find out first derivative with respect to x then we find out 2nd derivative with respect to…

Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: What happens if you can write a function as a composite in differentways? Do you get the same…

A: 39. Part a). It is given that, y=cos u and u=6x+2 Therefore, dydu=-sin u  and  dudx=6 So,…

Q: Determine the solution for this DE 1.) du/dx = (u2-x2) / (x2-u2 ) , u(1) = 0

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Q: 35. Given that d = 6(sin 2x - cos 3x) and y = 0 dx when x = 0, y = A -3 cos 2x - 2 sin 3x – 3 B 3…

A: We can solve this problem using initial value problem.

Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos…

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Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: 2. [ (1–3x)sin(}x)dx 4w dw 3. [* w°e™ dw w²e* -1

A: This question is taken from the definite integral in which we have to find the integral of the given…

Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

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Q: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

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Q: 1. Eliminate the parameter tgiven x = t – 3 sint and y = 2 + 3 cos t.

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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Q: (4) find dy if 3って - ソ= e* (2Co83x +3Sin3x) e = Sin (x+3y).

A: Given 1. y=e2x2cos3x+3sin3x 2. e2x=sinx+3y

Q: 2. If y = 3 sin(2x + 3) show that y" + 4y = 0

A: Given function is: y=3sin(2x+3) To show y''+4y=0 Finding first derivative of  given function:…

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: 13. y = -3 sin 2mx 15. y = -sin ix 14. y = -2 sin mx 16. y = -sin jx

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Q: 5.S Vsin 2x . cos2 x dx

A: Integration is a process of adding up infinitesimally small pieces of an area. There are mainly 2…

Q: 4 sin (In t) cos`(1nt) dt 5.

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Q: 1. (2xy + x²) dy + (2xy + y²) dx = 0 A2 (3x² + 2xy) dx + (x²) dy = 0 *AA 3. (3x²y³ + 3 sin x + 4y)…

A: Disclaimer: SInce you have asked to solve only question 3, this question has been solved only.…

Q: III. EVALUATE THE FF. ITERA •rU/2 ptan y sec y 1. . x' cos ydxdy Jo . cosy sin2x dy dx xp, •3n /2 pn…

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