Given y₁ (t) = ² and y2(t) = t−¹ satisfy the corresponding homogeneous equation of t²y" - 2y = t³ – 3t. t > 0. the general solution to the nonhomogeneous equation can be written as y(t) = y(t) + C₁y₁(t) + c2y2(t). Use variation of parameters to find y(t). Yp(t) = Preview

Q: (c) A function y(t) is a solution of y' + ky = 0. Sup find: (i) k (ii) y(t)

A: It is differential equation problem

Q: Find a particular solution to

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Q: Solve y''+2y'+2y=δ(t−1) +U(t−2), y(0) = 2, y′(0) = 1.

A: Given The given differential equation is y"+2y'+2y=δt-1+Ut-2. y0=2, y'0=1. Apply formula Laplace…

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A: The solution are next step

Q: If y(x) is a solution of (1-2-2xy +42y = 0, find the value of y'(1).

A: It is given that yx is a solution of 1-x2y''-2xy'+42y=0. The objective is to evaluate y'1.

Q: Find a particular solution to y" + 4y' + 3y = -16te²".

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Let a + 0 be any real number different from 0. If y = f(x) is the solution of y" – ay" = 60 – 60ax,…

A: Sine the statement true for any non zero a so we can choose a=1

Q: Consider the nonhomogeneous linear equation y" +9y' g(t) with the complementary solution y,= c1y1(t)…

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Q: If y, and y₂ are linearly independent solutions of t^2y" + 5y' +(2+t)y = 0 and if W(y₁, y₂)(1) = 3,…

A: Given differential equation is t2y''+5y'+(t+2)y=0   Also, given y1, y2 are Linearly Independent…

Q: Solve y (t) + 5y (t) + 4y(t) = h(t); y(0) = 0, y (0) - 2 where h(t)%3D tfor0 s t S2 h(t) = (2t +…

A: A differential equation with the initial conditions is called an initial value problem. In this…

Q: Let Y(t)= X(t) be the solution of , ly(t). 6 - 1 Y' = -2 Y, Y(0) = 8 5 4 Write y(T/10), round your…

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Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

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Q: • ex+y -2y-2=Ce e2x+y +2y-2%3DCEY e2xy -2y+23DCEY

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Q: 3. Find the solution of the DE 2yy" = 1 + (y')², x > 0, y > 0.

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Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Find the solution of y" – by' + 9y = 16 et with y(0) = 2 and y' (0) = 1.

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Q: Find the general solution for the following differential equation: y' + 2y = 5e-t – 3t y(t) =

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Q: The function u depends on two independent variables: u= u(x, t). Find the general solution of the…

A: Given: The function u depends on two independent variables: u=u(x,t). PDE: ∂2u∂t2+∂u∂t+u=2t-x. To…

Q: find the general solution of y''+y=cos(t) using the variation of parameters method

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Q: Plz asap handwritten solution acceptable Will definitely upvote

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Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

Q: Solve: x" -x+ 5 y'=t y" - 4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: What is the equilibrium solution of the equation y '(t) = 2y - 4? Is itstable or unstable?

A: The equation given is y't=2y-4. To find the equilibrium solution of the equation y't=2y-4.…

Q: Find the general solution of d²y x(x +2) dy + (x + 2)y(x) = x³, dx dx? given that y, (x) = x and…

A: The given differential equation is solving through the variation of parameters below.

Q: Find the general solution for the following differential equation: y' + 4y = 5te-3t

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Q: y" – 3y' + 2y = 2x² + 1

A: The Solution is given below

Q: Consider the general first-order linear equation y'(t) + a(t)y(t) = f(t). This equation can be…

A: Given below the detailed solution