(). %3D e2(s-6)²+25)) u (t – 2) (cos 5t + sin 51) O u(t – 2)et cos(5t – 10) ,6t | - u (t – 2) er-12 (cos(5t – 10) + sin(5t – 10) u (1 – 2) e6 (cos 5t + sin 5t) u (t – 2) e-61 (cos 5t - | sin 51) O ebt (cos 5t-sin 5t) u (1-2) e+12 (cos(51 + 10) + 응sin(5r + 10)

Q: (1+iV3)"+(1-i/3)" %3D 2n+1 Sin(- 3 2" Cos( ) 3. 2n+ Cos( 3. 2" Sin 3. (1-V3

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: b) 6(sin x)² + cos 2x + 1 = 0 [0,2π] I

A: Solution6 sin2x+cos 2x+1=0we know cos 2 x= 1-2 sin2xput this value in the given equation,6 sin2 x+…

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: The solution of (e+2xy?) dx + (2 cos 2y + 2x?y) dy is given by (A) e + x?y? + cos 2y = c (B) e +…

A: To find The solution of the given differential equation.

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: and if f(x) = sin" (x²) Lim 0 find 2m + n f(x) f'(x) (1 − cos x)m - = 2√√√3

A: Given that                                                            Formula:…

Q: (sin())= d.r

A: We apply chain rule here .

Q: 2sin?(®)+ Зсos(ө)-3-0

A: This is a question related to solving polar quadric equation. Here as a root we will get theta…

Q: I need help with proving this identity

A: LHS=RHS Show in explanation section.Explanation:If you have any problem let me know here in comment…

Q: L' (s²+4)(s²+9) 3 f cos(2a) sin[3(t – æ)]dx O b) cos(2t) sin(3t) c) None of these 1 * Só cos (2a)…

A:

Q: |(5e" + 5x4 =. + 9 cos x)dx 5et + x + 9 sin x + c 5ea + x + 9 cos x + c 5e + x³ – 9 sin x + c O et –…

A: Need to find integration

Q: Find L-1 {In (1 + s²) }

A:

Q: (D² - 9)y = 0. (A) y = e*(c,cos2r +c sin2x) B y = c,cosh 3x + c,sinh 3x y = c,cosh – 3x + c,sinh 3x…

A: Solution

Q: 4 L-1 s3 + 4s (A) [1 – cos 2t] (B) [1 – cos 2t] (C) [1 – sin 2t] (D) 1– cos 2t (E) [1+ cos 2t]

A: Given L-14s3+4s

Q: cos(2x) dx 1 In |1 – sin(2x)|+c 2 - 1 – sin(2x)

A: Note: It is assumed that the question is asking to test of the validity of the given equation.   It…

Q: ( sin(3x+1) cos?(3x+1) Evaluate

A:

Q: (9) If sin(A) = /2, sin(B) = - ½, "/½ < A < r, and n < B < 3*/2, find cos(A + B) (A) 0 (B) /2 (С) —…

A:

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

A:

Q: Find the solution for L{e-3t(cos(5t) – sin(5t)}. Find the solution for L-1{E + 10}.

A:

Q: 3e" + 3x + 10 cos x + 2)dx .2

A:

Q: Evaluate cos (x (x2 – 2x + 1) (2x - 2) sin (x 2 - 2x +1) (2 – 2x) sin (x? – 2x + 1) O (2x 2) cos (x-…

A:

Q: 1) - 3dx 2) (2-3x)² dx 3) x sin (2x2 - 1) dx (2x-3)2 4) sin3x cos² 3x dx

A: Step 1:Step 2: Step 3: Step 4:

Q: a) f(4x)dx x)cx

A: ∫02f4xdx Now, solve the above integral, ∫02f4xdx=∫01f4xdx+∫12f4xdx=f4·1-f4·0+f4·2-f4·1=f8-f0=1-0=1…

Q: Which of the following is a possible equation for the following trigonometric function?

A: To find which of the given equation is possible equation for the trigonometric function.

Q: Which of the following integrals represents the area of the intersection of r = 5+5 sin(0) and r= -5…

A: Given that  The regions  To find the area between the regions

Q: What is an equation for the cosine graph shown below? -135 -90 -45 -11 -10 +9 8/ -7 -6 -5 3 2 1 45…

A: Given query is to find the cosine equation of the function.

Q: [sin³ (2) cos(4) dx

A: Follow the procedure given below.

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

A:

Q: (c) L-¹ 2s 14 { (8+3)(8 + + +28+5) 4e-3s -1 s² (s+4)) (d) L-¹ {

A: As per the policy of bartleby the provisions is to solve only one question at a time  but here  I am…

Q: The square root of (1 2i) is (1) V5 (cos (+ 2n)+ i sin (5 + 2n")) for n = 0,1 COS (2) V5 (cos (+ 2)…

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: cos(2y) – 3x?y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0 %3D

A: Let's find.

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.