Solve the following Fredholm integral equations by using the successive substitutions method: 1. u(z) =+ ztu(t)dt-

Q: 3 "(x) = -x + x ²₁² = 1 √ ₁ ( x −t)³u(t)dt, u (0) = 0,u'(0) = 1.

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Q: Solve the following differential equations with Laplace transform method. d²x(t) dx(t) +5- dt +…

A: The Laplace transform of the function f(t) is denoted by Lf(t) or F(s), and defined as…

Q: Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation…

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Q: 2. y" - 6y +9y = 2 sin 3x; y(0) = 1, y'(0) = 1

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Q: Solve the differential equations by applying Laplace transform. i. y' + y = 8(t – 1), y(0) = 2,

A: We will find out the required solution.

Q: Q1/ Determine a complete solution of the following system of the WARITH AL-AN differential solution…

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Q: Determine which of the following sets of vectors is a basis for the solution space to the…

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Q: Use the method of Laplace transforms to find a general solution to the differential equation below…

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Q: Solve the following differential equation by using the Laplace transform techniques. d²x +8- dt² dx…

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Q: 3. y" – 2y' + 10y = e-* sin 9x , y(0) = y'(0) = 0 %3D

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Q: Use the Laplace transform to solve the given system of differential equations. d2x dy +5 dt + 5y = 0…

A: Here we have to find out solution of system of differential equation using Laplace transform method.

Q: 13 u(x) = 1 xtu(t)dt. %3D -x 3

A: The  Fredholm integral equation given as: u(x)=13x3-14∫01xtu(t)dt Here use approximation method to…

Q: Solve the following differential equation using Laplace transform method d²y dy dt +7+ 10y = 4te¬3t…

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Q: use Laplace Transform to solve the following differential equation d²y(t) + 6) + 8y(1) = u(1). (0) =…

A: differential equation:d2ytdt2+6dytdt+8yt=ut; y0=0, y'0=1We have to solve the differential equation…

Q: Solve the following sets of differential equations using Laplace Transform. x' + y=0, 3x+ y = t,…

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Q: (a) 으-2y %3D3,y(0) %=D 0 dt

A: Given: a) dydt-2y=3,  y0=0            b) dydt+5y=2,  y0=0            c) 3dydt+y=2,  y0=0 To…

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

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Q: 11 u(x) = atu(t)dt-

A: The given equation is, ux=116x+14∫01xt utdt                   .......1 On comparing the given…

Q: 3. Solve the following differential equations using Laplace transforms: 1 dx d²x dx +4 dt² dt +4x=t²…

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Q: Solve the following differential equation using Laplace transform method d²y dt2 dy +7+10y = 4te¬3t…

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Q: Solve the following differential equations by Laplace transform: y" + 2y' + 5y = 50t – 150, У (3)…

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Q: 18. u(x) = cos-11 | zu(t)dt- - TI +

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Q: Use the Laplace transform to solve the given system of differential equations. dx/dt=x-2y dy/dt=5x-y…

A: The given system of differential equation are

Q: Consider the following system of differential equations dx dy dt? dt dt dy , dy dx 4 dt %3D dt? dt…

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Q: Solve the following differential equations d²x +12dy +6x = 0 dt? dt? d x d?y 5- +16 +6y=0 dt? dt? by…

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Q: Solve the following partial differential equations. az = z + x? ay az (x + y²)+ y ax

A: Given, x+y2∂z∂x+y∂z∂y=z+x2---1 Lagrange's auxiliary equations will be dxx+y2=dyy=dzz+x2---2

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

A: on solving this we get the

Q: Use the Laplace transform to solve the given system of differential equations. d?y dt? d²x %3D dt?…

A: Given,  d2xdt2+d2ydt2=t2. . . . . .1d2xdt2-d2ydt2=6t. . . . . .2x0=5, x'0=0,y0=0, y'0=0 Now (1)+(2)…

Q: Solve the attached integral problem

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Q: dell t u(at,at) =0 tE (-e,*) e

A: According to our company policy, we are supposed to answer only one question at a time. For the rest…

Q: Use Laplace transforms to solve the differential equation ,, Y +6y' + 13y = 0, given y(0) = 3 and y'…

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Q: Solve the given differential equation using Laplace transform method: d²y dy dt2 + 6y = e-'; given…

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Q: Use the Laplace transform to solve the given system of differential equations. dx/dt = 4y +e^t…

A: The answer is as follows:

Q: Use Laplace transforms to solve the following differential equations. (4) y" – 6y' + 9y =t with y(0)…

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Q: Find the solution of the following ordinary differential equation using Fourier transform. du + eu =…

A: Consider the given ODE d2udx2+εu=e-x

Q: Solve the following ordinary differential equations by using Laplace transform. y" + 4y' +13y = 12et…

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Q: Solve the following differential equation using LaPlace transforms d²y dt2 dy + 4 +4 y = 0 with y(0)…

A: H

Q: Solve the following differential equations using Laplace Transforms y" +2y'+5y=5 y(0)=0,y'(0)=0 1.

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Q: 2П u(x) = ( ²5 - Ln (2+√3)) x 3 x + Sec (x )Tan (x) - [³ x t u(t)dt

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Q: /4 6. u(x) = sin (2r) - zu(t)dt-

A: To solve the integral equation using direct computation method.

Q: Use the Laplace transform to solve the given system of differential equations. dx dt dy = 5x - y dt…

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Q: y" + 4y' + 3y = 1– Uz – U4 + Ug , -

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Q: Find the solution of the following system of differential equations by Operator method or Laplace…

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Q: Use the Laplace transform to solve the given system of differential equations. dx/dt=-x+y dy/dt=2x…

A: Consider the given differential equations and initial conditions,

Q: Consider the following. dt (4 + t? Let t = 2 tan(0) and determine the following. 2 sec-(0) dt = de t…

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Q: (1+/t)dt + t/t ds = 0;when t = 1, s = %3D %3D

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Q: Use the Laplace transform to solve the given system of differential equations. d2x/dt2+5dy/dt+5y=0…

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 following differential equation by using the Laplace transform techniques. dr² dx +8. dt…

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Q: Use the Laplace transform to solve the following system of differential equations. dx = x - 2y dt dy…

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