2. Let 1 1 (–18 sin t – 16 cos t 0 3 0 1 A = f(t) = -25 cos t 1 -25 sin t Find the general solution to ' = Aã + f.

Q: 3. Obtain in two ways the general solution of (r + sine - cose ) dr + r (sine + cose ) de = 0

A: Use substitution method

Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: Find all values of x in the interval [0, 2π] that satisfy (cos x)2 − 3 sin x − 3 = 0

A: x=3π2 is the only values that satisfy the given condition see the calculation below

Q: Solve for the value(s) of x over the interval 0 < x < 360 2 cos x + 1 = 0 %3D

A: We have to find values of x over the interval 0&lt;= x &lt;= 360 of the equation 2 cos (x) +1 =0.

Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

A:

Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

A:

Q: Solve for x, if 0 <x S2n, Write your answers in exact values only. sin x +2sin x cos x 0 3 Tt TC 2 2…

A: simplify the equation and find the value of x

Q: 8 sin (2t) + 14 cos (t) = 0 for all solutions 0

A: Given equation 8sin2t+14cost=0Solution :8sin2t+14cost=082sintcost+14cost=0…

Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: Can i get help step by step with this problem?

A: Recall the following facts.

Q: Find all solutions to 2 cos(0) V2 on the interval 0 < 0 < 2A = |

A:

Q: 19 18. sin x cos x dx 1-3cos 2x dt 1+ e-t

A: The given integrals are;  19) sinxcosx/(1-3cos2x)  18)1/(1+e-t).

Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

A:

Q: If k 0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to ¹(3 cos(kr) cos³ (kr)] + C

A:

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

A:

Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

A:

Q: 9. The position of a moving particle as a function of time is given by: x = (4 - 0.11) sin(0.81)…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: dt cos (2 sin 21) /1– 4r

A:

Q: (3+ 7cos (x)) sin? (x) de 28. 29. sin° (9y) sec² (9y) dy / tan" (2) cos" (2) dz 30. [tan(2t) – sin°…

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

Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

A:

Q: 3- If a y + sin y + arctan a = sin 1 then what is the value of at (0,1)? dz -2 b)- 1+ cos 1 -1 1 a)…

A:

Q: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: 1.14 To determine L sinh(3t)cos (t) , f(t) = sinh(3t)cos? (t) must be rewritten as %3D - e sinh( 3t)…

A: Laplace Transform Definition: Given a function ft defined for all real t≥0, the Laplace transform of…

Q: 1. Determine the value of cos(2x+2y) if sin z 3 and tan y = - for 4 sysa. for 0sxs: VI VI

A: Given : sin x = 3/5 and tan y = -3/4

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: 1 ao et/2 dt = 0.50 2 An e-1/2 cos 2nt dt = 0.504 1+ 16n? 8n b, = et/2 sin 2nt dt = 0.504

A: a0 = (1/π) ∫0π e-t/2 dt , put -t/2 = x , dt = - 2dx Using formula ∫ et dt = et + c a0 = (1/π) ∫ ex…

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

Q: assume cos(t)=-1/4 where pi/2<t<pi cos(-t)= sin(t)= sin(-t)= sin(-t)+cos(-t)=…

A: Given:

Q: When the general solution of y" + 4y = tan2x is written as y = U(x)cos2x + V(x)sin2x then which of…

A: The given differential equation is y''+4y=tan2x. The auxiliary equation of the corresponding…

Q: 1 6 -8 sin(t) + 4 cos(t) + 4 sec²(t) – 2e' + dt = 1+t?

A:

Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

A:

Q: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

A:

Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

A:

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: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

Q: 7 (a² +b°) 1 Prove that : dx = ở (a sin x+ b° cos² x)' 4a’b?

A:

Q: 7 a Show that for all positive integers n: 27 2n sin nx dx = 0 ii cos nx dx = 0

A:

Q: Find all solutions to 2 cos(0) = V3 on the interval 0 < 0 < 2n %3D 0 =

A:

Q: Find all solutions to 2 cos(0) - V3 on the interval 0 < 0 < 2n -

A:

Q: 4. Prove that the identity is true. 1- cost e = sin² 0 1+ cos e

A:

Q: Find all solutions to 2 cos(0) = v2 on the interval 0 <0 < 2ñ 0 =

A:

Q: integrate cos^2(t)*sin^2(t) from 0 to 1

A:

Q: 0.5 COS T - In(4 sin z) dz. J0.1

A:

Q: A particle moves such that its velocity at time t is given by: v = 3t2i + 2 cos(4t)j + t2k If its…

A: given velocity of the particle at time 't' v=3t2i+2cos4tj+t2k initial position x(0)=2i

Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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.