(xiv) f(t) = 3+et – te-2t + e5t cos3t + 6sinh7t

Q: 1. f(t) = 5(e^-4t)[cos(10t)] A. (5s – 20) / (s^2 - 8s + 116) B. (s - 4) / (s^2 - 8s + 116) C. 50 /…

A: Laplace transferom of the function

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

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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: 1. F{(t³ – 3e*)²} 2. Ąe-2"cos3t + 5e-2'sin3t} 3. A(t² – 4t + 2)e³} 4. {3t*e¬6*cost} 5. A4t²sint –…

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Q: The general solution of y" - 2y' +y= e* cos(x) is

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Q: The solution to the initial value problem, y" + 4y' + 5y = cos cos 9x, y (0) = 0 is y (x) = ? ye(e,…

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Q: Find the solution of the initial value problem y" + 2y + 5y = 24e-t cos(2t), y(0) = 4, y'(0) = 0.…

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Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: 2. Solve the initial value problem + 3x? ) dæ = (cos(y) – e" Vr³ + 1) dy, 2Vx³ + 1 where y(0) = 0.

A: Check whether the equation is an exact equation or not. If it is true, then use the formula of…

Q: a) z=cos² (3 xy) onde x=p+eº ey=p²-2e³8 b) z=4x³y onde x=3p²+0² e y=p²-40²

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Q: 2. Find a particular solution using Undetermined Coefficients to: y" + 2y' – 3y = f(t), where f(t)…

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: Solve the initial – value problem: xtan sec2. dy C :y(3) =0 2. eesc?ydx-Vr sinydy =0 :y (In's)= 3.

A: we can solve these question by variable separation and homogeneous function technique of solving…

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: If the function f (x) solves the initial value problem dy = (x + 1)-1/2 – r dx - T. cos(T2) y(3) = 2…

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Q: Find the general solution. 1. (e2y – y cos xy)dx + (2xe2y – x cos xy + 2y)dy = 0

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Q: cos (2t + ) dt e21-3 -3 e 4 64e3 7 e-3 4 7 e3 4

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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: 2x Find the general solution of y" – 4y' + 5y sin (2)'

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: 4. g(t) = e³t + cos(6t) – e³ªcos(6t) 5. f(t) = tcosh(3t) 6. h(t) = t²sin(2t)

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Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

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

A: Given equation is  cos(x)d2ydx2-(1+x2)dydx-2xy=11+x2 with y(1)=-1 and y(2) = 2 h = 0.25 To solve  -…

Q: (b) Find the solution for cos(x) − (1 + x²) x − 2xy = - - with the conditions y(1) = -1, y(2) = 2…

A: Note:-  For this problem if you want general solution for this problem then please resubmit problem…

Q: s+3 is equal to s2 – 6s + 45 | A e3tcos6t В e3t (cos6t + sin6t) © e-3t(cos6t + sin6t) D e3t(cosh6t +…

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Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

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Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

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Q: 1) The value of f t.e-3t. sin 2t dt

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

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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: Solve the initial value problem. ds = Cos t - sin t, s dt = 4 %3D

A: According to the company policy, I'll solve the first question. Please resubmit the second question.…

Q: a. Solve the initival value problem: y = 5 cos (2r)/(6+ 5y), y(0) = -1. -6+V36 - ( sin (x) + 10 2. A…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: az dz 10. Compute and for the following equation. dy ,3 eY + xz2 6xy*z³ %D

A: The given equation is: ezy+xz2=6xy4z3...(1)

Q: 1. [8te" dt 2. . (1–3x)sin(}x)dx 3. w'e*™ dw 1-1

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

Q: 4s+5 b) Find L[eª“ f' (=cos 2) dt] and L-1 l(s-1)²(s+2)]

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Q: ds Find the particular solution of dt H|2 1 = cos-t

A: The given equation is;  ds/dt = cos (t/2).

Q: 1) Se2t cos(e') dt

A: Consider the integral  ∫e2tcosetdt

Q: Let y(x) be the solution to the initial value problem y" + 2y' – 3y = = -130 e-A" cos(5.x), y(0) =…

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Q: Solve the initial value problem: dx/dt+2x=cos(5t) with x(0)=5 find x(t)

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Q: 3. (1+ 2y²)y' = y.cos (x) diferansiyel denkleminin türü nedir?

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Q: 4. Find the general solution of y"- 4y – 12y = 5le sin(3r).

A: To find - Find the general solution of y'' - 4y' - 12y = 51exsin3x

Q: Q1:- Solve the following DEs:- ху?-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy -Зх dy 3) +…

A: We have to solve the given differential equation Here I am giving answer of 1st question if you want…

Q: Q3 Solve the initial value problem y" – y/ – 2y = 5 cos t, y(0) = 0, y'(0) = 1.

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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: (a) L{t + sin 4t – e2t cosh rt} (b) L{e' + cos 4t U(t – 1/2)} - (c) L-!{ s + 1 (s +2)(s² + 2s + 5)…

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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: (b) d²y dy Find the solution for cos(x) ² − (1 + x²) dx − 2xy = 12 with the conditions - dx² dx 1+x²…

A: Given cosxd2ydx2-1+x2dydx-2xy=11+x2y1=-1, y2=2, h=0.25`

Q: Solve the following initial condition problem: d2y/dx2 + 9y = 2 cos(3x); y(0) = 0; y′(0) = 1 /3

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Q: 2. Solve the following equations: d²y dy а) 8 + y = 2x + 40 sin x dx - dx2 d²y b) 2 dy + 2y = 2 sin…

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Q: Solve the equation (4y+2x– 5)dx + (6y +4x– 1)dy = 0 subject to the initial condition y(-1)= 2.

A: Consider a first order linear homogenous differential equation of the form, Pdx+Qdy=0→1 where P=fx,y…

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.