2COS X-I Sin x, Yna1 = 2cosxy, – Yn-1+ n21 and 0

Q: Prove that n r=0 "C, sin rx.cos (n-r)x=2"-¹x sin nx. 1

A:

Q: 3n + cos² . + 2n Prove that Limit + cos²P 2n cos²P p + r + cos?P 2 2n ...... 4r f= 1

A:

Q: H⋅w. and dwy for the following functions du OX ०५ 2 x+3y² e I_ _w=x²³ tan! ( _ x² + y² 2- W x+y √x²…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: r) x²(esinx) s) e*[ln (cos x)] (m sin 3x t) e2x x COS X u) ex リこ Sm

A:

Q: + tan dy 37 Ify = tan -1 -1 1 2 x +5x+7 1 2 1 2 1 2 x² + x + 1 +... to n term.

A:

Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

A:

Q: (n+1)x*! – x* . cos ((n+1)x) dx, where n is 4

A:

Q: Z1 "(cos(0, r2 Z2 02) + isin(0, – 02)](z2 # 0). 85. Let z1 = ri(cos 0, + isin 01) and z2 = r2(cos 0,…

A: Given z1=r1cosθ1+isinθ1 and z2=r2cosθ2+isinθ2.

Q: 5] What is the particular solution ( yp) of the ODE ( dx +y 4e*)? a) Ae* b) Ax³e-x c) Ax2e* d) Axe-x…

A: Question 1 is soly.It is against the policy of bartalby to solve more than 1 question. Here is…

Q: 8z Find where z = 4 sin(xy), z = te58, and y= 105-1088 dt O O O O dz = 4(10t5-10s8) cos(te5s…

A: We have to find  using given data.Concept required:If  then while finding we will consider  as a…

Q: Find the divergence of U=r cos(0)a-sin(0)a+2r²sin (0) a r 2cos (0) 3 cos (0) - r 3 cos (0) - 2cos…

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

Q: Prove that cos x cos y ≤ x - y for all x, y = R.

A: Mean value Theorem : Let a function  f:[a,b]→ℝ be such that    (i) f is continuous on [a,b] (ii) f…

Q: 6. For positive integer n, prove the following (given that I(½) = √√): √π = (2n)! √T. 4nn! T(n +…

A:

Q: Q Prove the following identities 1-sin (1) sec-tan ) 1 sin

A:

Q: Any individual providing psychology services to patients or clients needs the proper certification…

A:

Q: Find Z 2 order Sinz + 324 of the order of the zero at 2=0 pode of and 1-cosz 24 ot 2=0

A:

Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: find | cos*x dx 1 1 1 А) — — х —- sin2x + —x + — sin4x + c 4 1 B) =-x +- sin2x + X 4 1 8 1 x + sin4x…

A:

Q: 26) ) Show that the reductión formula for 1ー2 Sec" ndx = Sec atan n t n-2 n-- n-1 ) Hence use tta…

A:

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

A:

Q: (c). Consider the non-homogeneous ordinary differential equation y" + dy = 4e + 10e 0. Find a…

A: Given non - homogeneous differential equation is ,…

Q: 2) Evaluate: x* cos(x 5) dx. (A) 1/4 sin(x 5) + C (B) 1/5 sin(x 5) + C (C) sin(x 5) + C (D) 1/5…

A:

Q: And periad of :- yatan 4x @ yosco 5 Cos 10X 2) "Q2 S Ske kch these famckan g- these fanction g- L ye…

A:

Q: 5 [x²² sec (2) com ³ (2) abr dx 7 2tan can ²2 ( 1 ) [7tan² ( 1 ) +1 + C (Α 77 11 7 2x + (-) == ² (7)…

A:

Q: QI: Choose the correct answer 1) f(3e*r - 6 sin(3x) + 10cse (2x)) dx = A)e - 2 cos(3x) + 5tan(2r) +C…

A:

Q: -1 L-1 [wcose+ssine` s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) 2}, w & 0…

A:

Q: 4s+5 b) Find L[eª“ f' (=cos 2) dt] and L-1 l(s-1)²(s+2)]

A:

Q: | (5e" + 5a* + 9cos r+ 2)dr O e* - a5 + cos a + 2 + c O 5e" + a -9 sin a + 2+ c O e +a5 - 9 sin z +…

A: Here we have to evaluate I=∫5ex+5x4+9cosx+2dx

Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: 1 x 2 - 3 - [23] · 0-1²- B= 02 Find the value of "x" so that Det (A) = Det (B) -2 02 1/2 O -(1/2)

A:

Q: Use residue to evaluate the integral 2л 3 + 2 cos 0 do 5 + 4 cos 0

A:

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.