f(t) = e¯3t cos ( at + cos ( 2at + 3 2

Q: 3. Evaluate: 12x dx (a) J2 2-1)* (b) F sin 20 de o cos 20 (c) L1; x2 dx -1 x+2 (d) S, 2x Vx2 + 2 dx

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Q: Find the solution to the Bernoulli Equation. (3siny - 5x)dx + 2x²cotydy=D0 O x³(siny- x)2 = Csin?y O…

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Q: Q6: Determine a particular solution of the equation d'y +4y 4x cos 2x dx Using D-operator method

A: The solution is given as

Q: 1- 2xy 7. y = %3D %3D ds e'-2t co dt 9,

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Q: D. Solve the differential equation using Laplace transform of y - 3y' + 2y = et ; when y(0) =0 and…

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Q: dy 2х + ху is separable. dx y2 + 1

A:

Q: cos(rw) 1+w²

A: Fourier Cosine Transform or Infinite Fourier Cosine Transform: Definition: Let be a function defined…

Q: 2. Evaluate a. [x'(2x° +5)' dx b. dx V1-7x c. [cos 3xsin 3xdr d. sin* 6x cos 6xdx e. [t* cos(2r'…

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Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: d²y Find the solution for cos(x) (1+ x²) – 2xy = with the conditions %3D dx2 1+x2 y(1) = -1, y(2) =…

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Q: Q4 B) Find y' for the functions cos(xy) + 3*+cos ly+ In(xy) + log-7 dy

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Q: x'e* cos 3xdx + -dy = 0 Vỹ - 1 %3D

A: In this question, we solve the separable differential equation by direct integral. the differential…

Q: 2. Find L{f(t)} if f (t) = = cos 4t + t-1/2 + e5t – sin 3t – 5t – 1.

A: We will use the formulas Lcos at = ss2+a2Leat = 1s-aL(sinat) = as2+a2L(tn) = n!sn+1 Hence we have…

Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

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Q: 1 Let y = -. Find dy and Ay at.x = 7 with dx = Ax = - 1. Enter the exact answers. dy = Ay =

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Q: :Q1: Use Laplace transforms to solve the differential equation d² y - 24Y + dy + 2y = 3ex cos 2xr,…

A: Given:  d2ydx2-2dydx+2y=3excos2x      ......(1) y0=2 and y'0=5 We want to solve the given…

Q: π/2 g(x) = 2x + 4 sin² x g(t) dt. - n 0

A:

Q: y = | 9t cos (t10) dt O A. 9/x cos (x°) B. 10/x cos (x) Oc. cos (x) 2 OD. 9 cos (x) - 9/ã sir D. 9…

A: on using the test we get option (D)

Q: Find a linear differential operator that annihilate the given function d) Sin5x + 10 cos5x e)…

A: (d) Given that y=sin5x+10cos5x We have to find a linear differential operator that annihilate the…

Q: O1 Find: fx³ cos x dx using Integration by parts b. ſ cosx? 2x dx using Substitution Method a.

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Q: Find a differential operator that annihilates 4e2" cos 3x + 3x²e5.

A: Let L be the differential differential operator that annihilates 4e2xcos3x+3x2e5x. Find L.

Q: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

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Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: Find the singular sol" of the differential eqh (P+1)² (y-px) = 1 -

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Q: dx 2а — У dt fip dt x + 2 cos(t)

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Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: Q3/ Solve the differential equation using Laplace transforms d2y dr + 16y = 10 cos 4x , given y(0) =…

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: Q6: Determine a particular solution of the equation dzy +4y 4x2 cos 2x dx2 Using D-operator method

A:

Q: dy 1- Solve = cos x + y, where y = dx 2.0 at x 0 take step size h = Ax=

A: Given,         dydx=cosx+y Where y=2.0  at x=0   and h=0.1

Q: :- x2 + 10x + 24 dx. 1+ cos2 (x) f(t) = %3D At what value of t does the local max of f(t) occur? t =

A: Given: ft=∫0tx2+10x+241+cos2xdx

Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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Q: 3. Integrate! 12e dt a) ] 5e041 -0.21 b) c) f- dx 6r dr 3r? .$1+ In 3x² d) [Vcot*0 •csc² 0 do 2+…

A: Using Methods Of Integration

Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: Q 3. A. Find 1. £(t2 – 4t + 5)u(t – 3) 2. y-y +2y cos 3x - sin 3x 3. E-- s2 s+1

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Q: Find the differential equation of the quartics : c^2y^2 = x ( x - a )^3 with c held as fixed.

A:

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: 1) Se2t cos(e') dt

A: Consider the integral  ∫e2tcosetdt

Q: g(x) - Stoc cos (x + t) g(t) dt = 1 [1- (π/2)]

A:

Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Given  data  xey+2z-cos(xy)+ey-ln2=4  ,  A(ln2,0) Also given  when x changes by (dx=0.01) and y…

Q: Find the general solution of the nonhomogeneous 2nd order ODE (Use the appropriate method) y" - 4y'…

A:

Q: Find a particular equation for: y(4) + 8y''' + 32y'' + 64y' + 39y = e-2x[(4 - 15x) cos 3x - (4 +…

A: The given equation can be written as, y4+8y3+32y2+64y1+39y=e-2x4-15xcos3x-4+15xsin3x it is also can…

Q: 1. f(t) = cos(6t) 2. f(t) = (e^(8t)) cosh(3t) 3. f(t) = (t^2) e^(-4t)

A: Lcos(at)=ss2+a2 Leatcosh (bt) = s-a(s-a)2-b2 Ltneat = n!s-an+1

Q: • T/2 /2 36 sint t cos t dt = 3°|E|| %3D -1/2 -x/2

A:

Q: (у — сos-x)dx + cos x dy %3D 0

A: The given equation is y-cos2xdx+cosx dy=0 rewrite it as y-cos2x+cosx…

Q: Find the differential dy of the given function.    y = x√(1 − x2)

A:

Q: Find the solution of dx - (1+2x tany) dy = 0

A: Given: dx-1+2xtanydy=0