2πT S. 2+ 0 1 2 + cos² (t) - dt.

Q: 4. [cos(2y) - 3x2y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0

A:

Q: If y = cos ¹ prove Zyy + z = 0. )Z = (1 + i)(2-1)-¹, find |Z|.

A: Here given y=cos-1(z/x). We prove that zyy+z=0.

Q: cos (z) = e+1 elz+eiz 2i elz+eiz e+e- 2i

A: The objective is to find the value of cosz.

Q: S e-t cos(e-t)dt 3.

A: we need to integrate ∫0πe-tcose-t dt   we can do this integration by substitution.

Q: 1. Given the DE as x(1 – siny)dy = (cosx – cosy – y)dx a) Prove if the given DE is exact or…

A: Given differential equation: x( 1- siny) dy=( cos x-cosy-y) dx

Q: 5. || x+y cosx 1+sin x

A: Solution

Q: cos(x + y) dx + [3y² + 2y + cos(x + y)]dy = 0 %D

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have

Q: 11 a2 uis- こん 3. t cos X = 5 + CoS 20

A:

Q: Ex. 14. Find Lt (cos Vr+1- cos Vx) x- 00

A: Introduction :

Q: a csc 0 /2 co π/4 Jπ/40 p³ sin²0 sin o dp de do

A:

Q: Find L-1 () and L(t cos(3t)). s+7,

A:

Q: Enter the notation for each graph. C or K Example:C5 Eaxmple:K6

A:

Q: Consider the following DE: ( ½ + y + y5 sin x) dx + (6xy5 — 5y¹ cos x + e³)dy = 0, where a . (a)…

A:

Q: Show that (i) | te 3 sint dt 50 -3t %3D

A:

Q: 5.. Find the general solution to the DE using the method of Undetermined Coefficients: y" – 4y = te'…

A:

Q: L[(1 et + 3e-4t) cos 5t] = Find cm - b + na S s²b (s+a) - b mns +

A: Solution: Given  that  ℒ{(1-et+3e-4t)cos(5t)}=ss2-b+(m-ns)(s+a)c-b………(1)Let  f(t)=1-et+3e-4tNow,…

Q: (cos t)y" + (sin t)y' – ty = 0,

A:

Q: [a csc ()- y] do + ædy = 0 CSC O y= x cos(In z) + C O y=D cos (In a + C) O In + cos(E)= C O Ino COS

A:

Q: 3. Find: d (a) cos(t) dt xp 4

A: The given question is from the topic of Integrals

Q: 2 2 (5 cos? r* sin 0 drdodo: Tame 0 01

A:

Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: Consider the IVP y"(t) − 2y'(t) + 5y(t) = 0, y(0)=-1, y'(0)=3 (a) The characteristic equation of the…

A:

Q: 10 1. Reflect AABC over the line y = x and label the image AA'B'C'. Rotate triangle AA'B'C' 180º…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 16 cos 6nt dt = [

A:

Q: L a d 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: Find the solutions between [0,2r ). tan x+ tan x = 0 а. b. 2 cos (x) + 3 sin(x) – 3 = 0

A: a. tan2x+tanx=0 Take tan(x) as a common, tanxtanx+1=0 tanx=0 or tanx+1=0 tanx=0,-1 We have to find…

Q: Find the general solution to the given Euler equation. Assume x > 0 x2y" + xy' = 0

A: Given: x2y"+xy'=0 To solve this , substitute x=ez then the above equation reduces to DD-1+Dy=0 ,…

Q: Calculate $ |z|=1 z²e¹/z cos(1/z) dz.

A: