1) Solve U = Uz + U, u(1,t = 0) = sin(e¯² ) cos z, COS T, %3D %3D

Q: sin (t) -dt 3 (4+ cos (t))?

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Q: b) S sin 2 x cos x dx

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Q: f(csc x cot x + 3x2)dx csc x – x3 + c csc x + x3 + c - csc x + x3 +c .3 x° + c O cotx + x3+c

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Q: 3 4) Find / sin (2x) cos (2x)dx

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Q: z 3e*3S,y 3z2 + sin(z)s G dx

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Q: y=sin(x−y)

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Q: 1. find the linear approximation tof (x) at x = xo. Use the linear approximation to estimate the…

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Q: How would this parametric function of x=2cost +cos2t; y=2sint-sin2t be solved

A: In order to solve a parametric equation, firstly differentiate x and y with respect to t and then…

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: (h) (1 – cos² r) (1+ cot? r) = 1 %3D

A: you can clearly understand if you follow the below solution

Q: Solve dy/dx=sin(x+y)+cos(x+y)

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Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: (cos y+ ycosx)dx + (sin x –xsin y)dy = o

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Q: find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0,…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: 2) Proof that If y = f(x) = = cos x then dx sin x

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Q: Show that if y = V1 + sin x then sin x

A: We can solve it by doing derivative and make the proof.

Q: 2x – sin y y' = x cos y

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Q: +3x2 b. Find (y)? = sin³(cos³(* *3*)) %3D dx 2

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Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: b) S. cos x cos 7x dx

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Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

Q: General Sol. of  y' tanxsin2y= sin2x+sin2y is

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Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: y = cos³V2x – 1

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Q: Solve (cos x cos y- cot x) dx-sin x sin y dy = 0 %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.