Orthonormalize x,(t) = t ,x2(t) = t? and x3(t) = t3 in this order, on the interval [-1,1] where (x, y) = x(t)y(t)dt. -1

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

Q: b) Using Laplace transform, solve the system of differential equations dx 1, dt dy 4.x = 2H(t– 1),…

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Q: b) Use Laplace transform to solve the system of differential equations dr 4y, dt dy dt +x = y + 3e*,…

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Q: y"+6y'+9y= 0, y(0)=- 1, y' (0) = 6 %3D

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Q: y,(x) = ež, y',(x) = xe y" – y' + 0.25y = 0, a. Verify if the functions yı and y2 are solution of…

A: To check that a function is  a solution of a differential equation, if we substitute in the left…

Q: Solve the differential equation using Laplace Transform. (a) y" – 2y' + 5y = 8e'sin2t, y(0) = 1,…

A: a. The given differential equation is                                     y''-2y'+5y=8etsin2t   ,…

Q: Let g be continuous on [a, b), and let f(z) = S (* – t)g(t) dt. Prove that f is a solution of the…

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Q: y" + 4y = 0 ; y(0) = 2, y'(0) = 2

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Q: Solve the differential equation using the Laplace transform у" — 5y — бу %3Dеs", y(0) 3D 0; у' (0)…

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Q: Please solve the differential equation below. d²y(t) dt² +D dy (t) dt - + E y(t) = F dx (t) dt + G…

A: A differential equation is given by, d2ytdt2+D dytdt+E yt = F dxtdt+G xt with initial condition yt=0…

Q: b) Solve the given system of differential equation by laplace transformation dx = x- y dt dy — 5х -…

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Q: y"(x) + 9y(x) = 40e* ; y(0) = 5, y'(0) = -2

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: SOLVE THE PARTIAL DIFFERENTIAL EQUATION BY LAPLACETRANSFORM uz(x, t) + u¿(x,t) = sint given that…

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Q: Q:- solve the differential equation by Laplace transform : y" – 3y' + 2y = e3t %3D Where the initial…

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Q: What is the differential equation of the orthogonal trajectories of the family of curves X = Cy? А)…

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Q: Use F'(x) = dx g(t) dt = g(x) to verify that the indicated function is a solution of the given…

A: The given data is: y=x∫4xcosttdt To verify the indicated function is the solution of the given…

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: Linearize the following differential equation about point, x= T/3. d²x +2 dt? dx + sin x=0 dt

A: Answer:

Q: Solve the given system of differential equation by laplace transformation dx/dt= x - y dy/dt= 5x -…

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Q: azu(x, t) a?u(x, t) (-00 0) at2 ax2 u(x,0) = 4e-5|x| %3D (x,0)30 at

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Q: (x)1/2sin(y/x)

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Q: Solve the differential equation dx/dt-Mx=3emMt under the initial condition x(0)=M-2 by using the…

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Q: Verify that the given two-parameter family of functions is the general solution of the…

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Q: at f(x,y,z) = z exp(− x2 + y2 4z ) satisfies the differential equation ∂2f + ∂2f = ∂f ∂x

A: To prove that                 ∂2f∂x2+∂2f∂y2=∂f∂z Where,         f(x, y, z)=1ze-x2+y24z

Q: Use Laplace transform to solve the partial differential equation: d'y dy ox² at -+xt where y(x,0) =…

A: The given P.D.E is ∂2y∂x2=∂y∂t+xt where yx,0=0, y0,t=0 and yx,t is bounded for t>0 and x>0. To…

Q: Use Fourier transform to solve the partial differential equation: ди d²u ax² du(0,1) -10u: x>0,t> 0…

A: Given: The partial differential equation and the conditions are: ∂2u∂x2-10u=∂u∂t, x>0, t>0…

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? А)…

A: Find orthogonal trajectory

Q: Obtain the differential equation of the given family of curve: y² : C-x a. 2x³y' – 3x?y – y³ = 0 b.…

A: Given curve : y2=x3c-x ⇒c-x=x3y2

Q: Let g be continuous on [a, b), and let f(x) = S (x – t)g(t) dt. Prove that f is a solution of the…

A: Given that g be continuous on a, b and let f(x)=∫ax(x-a)g(t)dt. And we have to show that f is a…

Q: Solve the initial-value problem dx -2x – 2y dt dy -2x + y, dt where the initial condition (x(0),…

A: I have Transferred into a matrix differential equation and then solved

Q: b) Solve the given system of differential equation by laplace transformation dx/dt = x-y dy/dt =…

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Q: Determine the solution of the differential equation using Laplace and Inverse Laplace Transforms.…

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Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — уз %3 С? (1) (x +…

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Q: Solve the partial differential equation subject to u(0, t) %3D 0, и(1,t) — 0, t>0 и (х,0) — 0, du…

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Q: a2u(x, t) a2u(x,t) = 9. ax2 %3D at2 u(x,0) = 4e-51x| %3D a u (x,0) = 0 at

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Q: Solve the system of differential equations dx = 4 y +3 dy using differential operators of the form…

A: Givendxdt=4y+3     1dydt=-x+2     2Now differentiating 2 with respect to t⇒d2ydt2=-dxdtfrom equation…

Q: Solve the differential equation using Laplace Transform. (a) y" – 2y' + 5y = 8e'sin2t, y(0) = 1,…

A: According to the given information, it is required to solve the given differential equation using…

Q: azu(x,t) azu(x, t) 9- ax2 (-00 0) %3D at2 u(x,0) = 4e-5x| %3D

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Q: Let g be continuous on [a, b), and let f(x) = S. (x – t)g(t) dt. Prove that ƒ is a solution of the…

A: The given differential equation is                                           f''=g…

Q: Use Fourier transform to solve the partial differential equation: du d'u du(0, y) 01 du(x, y) əx " =…

A: Fourier cosine transform with respect to x Fcs=2π∫0∞fxcossxdx Inverse Fourier cosine transform…

Q: Solve the differential equation using Laplace transformation y" – 2y' + 3y = 2t²e3t where y'(0) =…

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Q: 3. Find the total differential of the ff. at (1, -1). f (x, y) = 3.x² + y² – xy %3D

A: Solution:Givenf(x,y)=3x2+y2-xyFormula:d(xn)=nxn-1

Q: SOLVE THE PARTIAL DIFFERENTIAL EQUATION BY LAPLACETRANSFORM u(x,0) = 0 u(0, t) = 0 u,(x, t) +…

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Q: Solve for the solution of the differential equation using Laplace Transform. Find f(1) y" +4y +5y =…

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Q: x"(t) + 9x(t) 5sin (2t) when t = 0,x = 3,x' = 1

A: Solve the differential equation by using Laplace transferom

Q: 1, 0<t <1 1<t < 2 y"+ 4y = g(t), y(0) = 0, y '(0)= 0, g(t) = {- 1, 0, 2<t

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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.