Let f (t) = te" + e t sin 12tFind L{f (t)}

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

A:

Q: tan (VT)+2 dx J Va (sec(VT) – cos(/7))

A:

Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: sin(2t + ) dt = 00 64e 4. O O OG

A: Here in this problem we have to find ∫0∞sin(2t+π2)e2t-3dt

Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: e5x cos e5x dx sin²e5x

A:

Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

A:

Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

A:

Q: 4x3 — 2х2 — х+5dx А. -2 TT 3 sin t 4 dt cos²t В.

A: Evaluate the integral using the second Fundamental theorem of calculus.…

Q: y = (sin x +cos x) sec x = sec² x

A:

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: If y = (3x)sin (2æ) then %3D dy dx (Be sure to express your answer in terms of x)

A:

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

A:

Q: Obtain the general solution to the equation. dr +rtan 0=7 sec 0 tan e de

A:

Q: Q No 4) Integrate S cosec³xdx . AND also Find F sin10xdx

A:

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

A:

Q: dr (c) (d) lim sint dt

A: Given:

Q: L[if i sin√2t dt²

A:

Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: show that the differential eguation is exact, then solre that method using 2 2 dy- x²-x+y? |

A:

Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: 1. [* sin' y cos' ydy 3

A:

Q: at æ = 0 for 12 sin(t)dt.

A:

Q: roo sin(2) Compute (4) dx. fo x(x²+4)

A:

Q: What is the first step in eliminating the parameter t from the equationsx= 3 1 sin t and y = cos t -…

A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: al equation sin(t) with y( solution for this hen t belongs to ||

A:

Q: tan st e dt 2

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

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

A:

Q: II. Solve th following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 %3D -

A: We are given a linear second order nonhomogeneous differential equation with constant coefficients…

Q: 2. xy' -y == y cos 3x

A:

Q: dx 1 + sin(ax) %3D

A:

Q: | sin t cos* t dt 9.

A: We have to evaluate given integral Concept:

Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

A:

Q: Find the solution of the equation z az cos y which tends to zero as x o and has the value cos y when…

A:

Q: - Tt/2 2 cosx dx 1+ (sin x)2 -T/2

A: Using substitution: So the limits of the integration would be given by: And

Q: tan (e) 1+z* (d) (22+ cosh 2z)dz () z coshz dz zp-

A:

Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

A:

Q: Find the solution of the equation = e Cos y ax ay which tends to zero as x → 0o and has the value…

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: 8. (sin°(5y)dy

A:

Q: c) Se- sin(4t) dt

A:

Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

A:

Q: 9. [sin Ssin' cos–dx 3 3

A: (9) To evaluate ∫sin5x3cosx3dx Substitute sinx3=u and cosx3dx=3du. Therefore,…