Find the general solution of du 2u + dt cos t t t

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin (3t), y…

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Q: *e(1+i)t dt

A: We have to find the given definit integral please see the explanation below..

Q: Evaluate the integrals

A: Given that, Evaluate an integral vector function by evaluating the integration of each component of…

Q: Solve the following differential equation using Laplace transform d?y -6- dt dy + 10y = cos(2t),…

A: Given- d2ydt2-6dydt+10y=cos2t To Solve- The above differential equation by using Laplace transform.

Q: Find the solution of the following differential equation by Laplace transforms: y"' – 5y" + 7y' – 3y…

A: Consider the following initial value problem and apply the Laplace transform on both sides:

Q: Q.5 If P=r cos t and rsin t-2te = 0, find dP/dt.

A: Given ,  P = r cost and r sint - 2ter = 0 We have to find dP/dt Since ,  P = r cost  Then ,

Q: 4. Evaluate + tyt - 1j+t sin at k) dt

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Q: Obtain the DE given the general solution . y = c, + C,x + C,x³ + (c, +c,x)e~Và« + (cq cos 2x + c,…

A: We will generate auxiliary equation from the roots of it

Q: Derive the working differential equation for the given circuit, R ww VR i(t) V(t) O iR+ L = E (t)…

A: Given that, There is a series RL circuit in which i is the current flow through the circuit. Voltage…

Q: (k) / te'dt (1) / e' sin(t) dt (i) e2t dt dt 1+ t2

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Q: 1. Compute d e (z²) (sin(t) + e*)v= dr

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Q: Solve the following problems by applying chain rule. dw (a) If w=x -2y² +z', and x= sint , y=e', z=…

A: We have to applying chain rule and solve given problem

Q: solve the following differential equation using Laplace transforms d^2y/dt^2+4dy/dt+4y=0 with y(0)…

A: We will write the given Initial value problem  in the following form:…

Q: Derive the working differential equation for the given circuit, R i(t) → VR V(t) O + iR= E (t) * +…

A: topic - differential equations

Q: Rewrite the following differential equation using differential operators. 1. y" dºy Зу" + 4у d³y 12e…

A: The given differential equations are  1) y"'-3y"+4y= 12e2x+4e3x  2) y"""+4y"'= 2tanx

Q: t F(x) cos(3t – 1) dt sin z %3D

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Q: Verify the initial value theorem of f(t) = 1 +e¯t[sint + cos os t]. 3 1 0 2

A: Solution :- As per guidelines I solve only first question .

Q: Solve the following differential equations by using Laplace transform. dy (b) 9. +y = te", y(0) =1

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Q: Find the solution of the following differential equation by Laplace transforms: y"' – 5y" + 7y' – 3y…

A: Consider the provided question, We have the find the solution of the given D.E by using the Laplace…

Q: Solve the following differential equation by using Laplace transform. dy +2y = 2-3e , dt y(0)=0.

A: GIVEN: dydt + 2y = 2 - 3e2t, y(0) = 0

Q: Solve the following differential equation using Laplace Transform: d?v(t) dv(t) + 4 dt + 4v(t) = e-t…

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Q: Find u from the differential equation and initial condition. du 1.8t – 1.6u u(0) = 1.1. = e dt

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Q: dv = 16 – v², when t 0, v = 10 dt

A: Given:

Q: Find dy/dt, x=4 sin t; y=12 cos t* O 24 cos t O -24 sin t O 12cos t O -12sin t

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Q: у" — 5у" + 7у' — Зу %3D 20 sin(t) , У (0) — у'(0) — 0, у"(0) %3D —2

A: Consider the provided question, We have the find the solution of the given D.E by using the Laplace…

Q: T 00 f(t) = + E an cos(nat/L) + b, sin(nat/L) (1) ÷TSt) cos(nat/L)dt, b =".S(t) sin(nat/L)dt (2) an…

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Q: 4. Find each differential. a. du if u = x² – e* b. dz if z = tcos(t), t = 0 and dt = .2

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Q: Use the Laplace transrorm to solve the given initial-Value problem. y" + 25y = cos(5t), y(0) = 2,…

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Q: Solve the following differential equations by using method of Laplace transform. b) y"+9y = 4e ;…

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Q: y" +2y'+y=1+3 y(0) = 1, y'(0) =0

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Q: In this question we work with the ODE dy +2ty = –T cos (T t) dt and initial condition y (0) = 0.

A: Given differential equation is, 1+t2dydt+2ty=-πcosπt The equation is rewritten as,…

Q: B. Solve the following differential equations using Laplace Transforms: 2. 9(dy/dt?) - 24(dy/dt) +…

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Q: Consider the following. dy dx ex — У, (0, 1) %3D y | || 5+\/|| -4 ///+1 | 4 I| |-3+ (a) Find the…

A: dydx=ex-y ,   0, 1 On simplification, we get dydx+y=ex Now comparing with dydx+Py=Q, we get P=1…

Q: y" -4y 0 y(0) = 0, y'(0)=0 %3D %3D

A: on solving this we get the

Q: d/dt [sec^3(t)] compute the derivate

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Q: - Find (i) L {t e“ sin bt} (ii) L{ tesin 4t dt

A: We will find out the required value.

Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…

Q: B. Solve the following differential equations using Laplace Transforms: 1. d'y/dx? + dy/dx -2y =…

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Q: Find j cos(VF +1 +1)dt dx

A: Using the leibnitz integration problem.. Explanation of the solution is given below..

Q: Solve the Bessel ODE d?y 4. dt? + e-0.1t . y=0, y (0)=1, dt dy (0) = 1 2°

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Q: Which of the following differential equations is separable? dy cos(ty) dt O dy = dt t cos(ty) dy =t+…

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Q: Find a differential operator that annihilates the given function x²e ¬*sin (2x). A ((D+1)²+ 2) 2 B…

A: The given function is  x2 e-(x) sin(2x) (.) Annihilating differential operator of x(n)       is…

Q: The two functions y1(t) = sin t cos t and y2 (t) = sin 2t are linearly independent. O True False

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Q: c) y = x² cos (t³)dt

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Q: Solve the following Initial Value Problem using Laplace transfo -9t y" - 12y + 11y = e ;y (0) = 1,…

A: The given equation is y''-12y'+11y=e-9t Taking Laplace transform on both sides Ly''-12y'+11y=Le-9t…

Q: Solve the following equation by Laplace transforms dx +3x=e dt given that x= 2 when t=0

A: Since you have asked multiple questions, we will solve the Question Q1 (a) for you. If youwant any…

Q: f(t) = (C + 1)te Bt sin At

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Q: Solve the following differential equation using Laplace transform d²y A. + 25y = 10 (cos(5t) – 2…

A: Given: d2y/dx2 + 25y = 10 [cos(5t) - 2sin(5t)] y(0)=1 , y'(0)=2 Repost the question B.

Q: 6. Let r = t sin t, y = t cos t, 0<t<1. dy (a) Find dr

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