y" - 4y' + 4y = e" |3D y(0) = 7, y' (0) = 0 the Laplace transform Y(s) of the solution y(t) is : %3D %3D

Q: y' (t) =

A: Here, the question it is posed to find out the central difference approximation that we must know…

Q: Consider the hyperbolic partial derivative equation Uzz = Uu – sin (x), rE [0, 1], t>0, with the…

A: Given,uxx=utt-sin x , x∈0,1, t>0Boundary conditions: u(0,t)=ux(1,t)=0 , t>0…

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t x(t) general solution function

A: Given equations are                                              dxdt+dydt+x=e-t           ...…

Q: Q: substitute derivation equation and derivation equation 2, in equation 3 ? [Me] =C(1– x)– p[Me,L,]…

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Q: [(2x -1)3– x )dx = + 8. 0 3.

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Q: 1 Differentiation of a complex function dw =f'(z)%3 Lim Sf(Zo+8z) – f(zo) Sz w =f(z) dz 8z-0

A: The given is the definition of differentiation of a complex function which is just generalized from…

Q: Solve Separable (x – 4)y*dx – x³ (y² – 3)dy = 0 -

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Q: solve differential eq by laplace transform the charge qt on capacitor in an lc series circuit is…

A: Consider the provided D.E,

Q: solve using laplace transformation  y'''+3y''+3y'+y=30x^2e^x  Find the particular solution given…

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Q: Can you show part b how to solve and more details

A: 1

Q: solve by using Laplace Transform y"-10y'+9y=5t, y(0)=-1, y'(0)=2

A: Use Laplace table.

Q: dy = y2-y that passes through the indicated points. dx Find a solution of x (a) (0, 1) y = (b) (0,0)…

A: The solution is given in the next steps.

Q: A local target store bought 116 pizzas at Pizza Hut for its holiday party. Each guest ate 1/6 of a…

A: Let x be the number of pizzas bought by the store and y be the number of guests target have for the…

Q: laplace y"(t) +9y = 40e, y(0) = 5, y'(0) = -2

A:

Q: y" = 2 Y y' = 5 + sin(y/x) 9x²y" = y + 3xy' 2xy²e(ry)² + 2x² ye(xy)² y' = 0 Choose... ✓ Choose...…

A: (.) Given differential equations are,(.)  First - order exact differential equation: A first order…

Q: Consider the functional (a) S[11, 12] = [ dr [7y/² + 24yy⁄2 + 21y2² + 4y{ + 12y192+9y²] . two…

A: (a) The Euler-Lagrange equations for the given functional are:For y₁:d/dx(∂L/∂y₁') - ∂L/∂y₁ = 0⇒…

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t     x(t) general function solutions

A: This system has been solved by the elimination method, by eliminating y to get the general solution…

Q: Using Laplace transforms. Solve y" + 4y′ + 3y = e^t. When, y(0) = 0 and y′(0) = 0. Whole Solution

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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: Sketch the graph of the solution and describe its behavior as t increases. 9/144) y" +y' – 2y = 0,…

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Q: 5) Find y(0.1) if y'=x-y² and y(0) 6) Use Euler's method to find y(0.4) given y' = xy, y(0) = 1. =…

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Q: Find dy/dx at the given point for the equation. x = y3 – 5y2 + 2, (-2,1)

A: Given, given point is (-2,1)formula of derivatives are '

Q: I" (D-x) (D +x) (y) =0, then the function y satisfies the DE O y"-x3y=0• O (y'-x) (y'+x) =0• O y"+…

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Q: ii) J(y)=[(e" *y")dx, y (0) 0,y'(0) =1,y (1) =e, y'(1) = 2e

A: Solution 2: Given functional is J(y)=∫01e-xy''dx, y0=0, y'0=1, y1=e, y'1=2e. To find the extremal of…

Q: (xy+y2) + (x2 -xy)(dy/dx) Homogeneous equations

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Q: 7. хЗуб + е1-х — cos(5y) %3D у?

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Q: equation: Using the Laplace transform method, solve for t≥ 0 the following differentia d²x dt² dx 5-…

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Q: y(0) =-1,y'(0)=2 2x SOLUE USING LAPLACE TRANSTORMS Y"- 24'-3y= 4x -5+6xe

A: Given  y''-2y'-3y=4x-5+6x e2x,    y(0)=-1…

Q: vi) J(y) = [(y," -y)dx ext, y,(0) = 2, y,(1) = 0, y (0) = 0, y,() 1, y, (0) 1, y,(1)=0

A: Solution 6: Given functional is J(y)=∫01y1'2-y2''2dx, y10=2, y11=0, y20=0,  y21=1,  y2'0=1,  y2'1=0…

Q: 3. Solve y" – 2y' + 5y = 0, y(0) = 5, y'(0) = -3.

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Q: Consider the initial value problem for function y given by, y" - 3y + 2y = - 8(t-3), y(0) = 0, y'…

A: Given differential equation: We have to solve the given differential equation.

Q: Use the Laplace Transform to solve the given initial value problem. y(4) - 4y=0; y(0) = 1, y'(0) =…

A: The given initial value problem is y4-4y=0; y0=1, y'0=0, y''0=-2, y'''0=0. We have to find the…