Consider the DE dx + kx – la? = 0, dt - where k, l e R+. Use a suitable substitution to transform the DE into a linear non-homogeneous equation, then derive its general solution.

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

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: : Solve the differential equation by using Laplace Transformation hod? у" — 4y' + Зу %3 0 у (0) %3D…

A: Taking Laplace Transform in both direction:

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: dx + dx dy e; dy = x +y Use elimination to solve: dt dt dt dt

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Q: dy y = sin h(2t),given that Solve the differential equation using Laplace transform dt2 y(0) = 0,…

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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: In each exercise, obtain the general solution. 1. dr/dt = -4rt; when t = 0, r = rg. 2. xyy' = 1+ y²;…

A: We solve these differential equations by separation of variables.

Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? ... (2) ev²…

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Q: Solve for an autonomous equation? dy/dt = f(y)

A: An autonomous first-order ordinary differential equation is an equation of the form

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

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Q: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

A: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

Q: The substitution V = In u can transform the differential equation (DE) dy/dx + y = 2(y In y) %3D %3D…

A: We have dydx+y=2ylny                    ...(1) Let v=lny Taking e on both sides: ev=elny⇒ev=y⇒y=ev…

Q: Find the IVP for the differential eqution X' y' - 3xy'+68y=0, that satisfies the initial conelition…

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Q: Find an integrating factor for the DE y( 4x – 3y – 3) dx +x(x – 2y – 1) dy =0. (A (B) y2

A: The given differential equation is in the form of Mdx + Ndy = 0 Where, M=y4x-3y-3 ; N=xx-2y-1 The…

Q: Solve the given system of differential equation by laplace transformation dx —х - у di dy 5х — у. dt…

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Q: Find the differential dy. (a) y = xV7-x dy (b) y = (1+x) dy

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Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: Find the two-term perturbation approximation to y" = e", y(0) = 0, (0) = 0. %3D

A: Given:                                    y"= e∈y                               y(0) = 0…

Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx+x(x+2y)dy =0 ? 2 A 2 B C x2 D

A: Given, (4xy+3y2-x)dx + x(x

Q: If r = sin ( ƒ(t)), ƒ(0) = p/3, and ƒ'(0) = 4, then what is dr/dt at t = 0?

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Q: Find the general solution of dt z(t) = Az where z = y(t and A =

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Q: y" x, Say=- Determine the solution to the differential equation using Laplace Transform: cosh t + 4…

A: We will find out the required solution.

Q: Find S t? e' dt using integration by parts.

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Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx + x(x+2y)dy =0 ? 2 (A 2 B x2 1 x2

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Q: Solve the Bernoulli equation for y by making the substitution u = dy = 4y + y°. dt Use the following…

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Q: What is the integrating factor of the linear DE of order one ydx + (3x – 2y+ 5) dy=0? 1 A x² B y3 C…

A: Given linear differential equation is y dx+(3x-2y+5)dy=0 ⇒dxdy+3xy-2+5y=0⇒dxdy+3xy=2-5y Which is…

Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx+x(x+2 y)dy =0 ? 1 A x2 B x2 2

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

A: Find orthogonal trajectory

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

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Q: R/c Po () In Derive Form 3 of the thermodynamic equation: %3D Dt To C„T DT from Form 2: c, Dt 1 Dp p…

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Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

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

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Q: Consider the dynamical system dx sin(x) dt dy = e – 1 dt Around the fixed point at (0,0), integral…

A: Given:-               Consider the dynamical systemdxdt=sinxdydt=ey-1 Around the fixed point at…

Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, ln (t + 1).

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Q: Use the fourth-order Runge Kutta method to solve for the velocity and position of the free-falling…

A: Given:- t=0 , x=v=0  t=4s

Q: Find the integrating factor of the given linear de and general solution of the…

A: Here we solve the given differential equation.

Q: Find the integrating factor of the given Non-Exact DE y (4x + y) dæ – 2 (x² – y) dy = 0

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Q: Obtain the integrating factor of (2* y² + v) dæ + xdy = 0 O ary 1

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Q: (a) Calculate the first-order differential equation below using transformation y = xv. dy +3у %3D 2х…

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Q: The total differential of g(x, y) = e*z²-y is at A(1,4) is %3D Select one: a. dg(A)=(8-1)e^(0) O b.…

A: Consider the following function: gx,y=e4x2-y Differentiate gx,y with respect to x taking y as…

Q: Apply the Laplace transform to the differential equation, and solve for Y(s) y"+ 25y = 3(t – 4)us(t)…

A: Given that, y''+25y=3t-4u4t-3t-8u8t, y0=0, y'0=0 To find Ys

Q: What is the integrating factor of the non-exact DE (4xy+3y²-x) dx + x(x+2y)dy =0 ? (A) x² 1 B (U) D…

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Q: Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy = y – t² + 1 dt

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Q: Find dz/dt dz/dt given:  z=xe2y, x=t6, y= -1+5t

A: Given,         z=xe2y    , x=t6     ,    y= -1+5tWe know that,            ∴dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

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Q: 12

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Q: A suitable substitution to transform the D.E. t dy – y dt = tydt into linear equation will be :

A: Substitution to convert given differential equation into linear

Q: Find the general solution to the following equations. dx dy 1. + y = x , = 3y dt dt

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Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? (2) ey² (3) x²…

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