Find the value of C that makes y = Ce−2x a solution to the initial valueproblem:y′ + 2y = 0,   y(0) = 3

Q: Use the method of undetermined coefficients to find one solution of y(t) y"-7y - 3y = 7e³t.

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Q: Find the general solution  y ′ + 4ty = ty2 + t

A: Given differential equation is  y'+4ty=ty2+t to find the general solution of this equation

Q: xdy + (3xy + y - e-³x) dx = 0

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Q: 1 (1 – 30, coefficient of 1 2y2/3 Solution: y2

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Q: Find a fundamental set of solutions {y₁(x), y2(x)} of the equation y₁(x) = Y₂(x) = dx² + 13 dy d.x +…

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Q: 2 2 dydx Әхду

A: Given: h(x,y)=4xey+3y+7

Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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Q: The equation y² = cx is the general solution of: y' = 2x y 2у В A y' = y 2y 2x O D B.

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Q: Determine two linearly independent solutions to x2y′′+xy′+(x2− 9/4)y =0 on the interval (0,∞).

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Q: Eliminate the constant: 3x 3x y=c^+c xe +c xe Oy"-6y'+9y=x y"+ 6y'+9y=0 Oy"-6y'+9y=0 Oy"-4y+3y=0

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Q: Find the solution of the initial value problem y00 + у %3D 5xе2х, у(0) %3D 1, у0(0) 3 0.

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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: у" — у' — х %3 0

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

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Q: dy Solve the initial value problem: + 2y = 6e¬x; y(0) = 8

A: Since the given differential equation is first order linear differential equation so we first find…

Q: Find the solution: 4 + 2y = 1, y(0) = 2.5. dt

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Q: Evalutate: limx→5 O-2 04 05 x-5 √x-1-2

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Q: Use undetermined coefficients to find the particular solution to y + 4y' + 3y = 2e² Y(t) =

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Q: Q1. Solve the initial value problem of first order linear differential equation: x ௗ௬ ௗ௫ + y = e ௫ ;…

A: Introduction: A first order linear ordinary differential equation is expressed in the form of…

Q: Find the solution. y'+=Vy. y(1) = 0 x-3+2x 2 - 2 A y = 9x 3 x3-2x 2 y = + 1 B 9x I+3x y = %3D 9x 3.

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Q: Solve for the solution of the DE: y(4) – 9y" + 20y = 0

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Q: If y = 2² is one solution of x²y" + 2xy' − 6y = 0, find the other linearly independent solution.

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Q: Solve the IVP y′′ + 4y′ + 13y = 0, y(0) = 1, y′(0) = −5

A: To  Solve the IVP y′′ + 4y′ + 13y = 0, y(0) = 1, y′(0) = −5

Q: : Find a solution op of the I.V.P.: Y₁ = −y₁, y₂ = y₁ +ty₂, y(0) = []

A: To solve this problem using the following steps  First we find the particular solution of the first…

Q: The solution to the DE y' + 4y = e-4t; y(0) = 2 may be expressed as y = teat+ beat; find b-a.

A: The given differential equation is          y' + 4y = e-4t   . . . . . . . . . . (1)  The homogenous…

Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: Solve for the solution of the DE: y(4) – 8y" + 24y" + 32y' + 16y = 0

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Q: y(4) – 8y" + 24y" + 32y' + 16y = 0

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Q: Find the particular solution of y2dx + x(x+y) dy=0., when x=1, y=1. Let x=vy

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Q: The equation y² = cx is the general solution of: y' = 2x y': %3D у 2y A y' = 2 2y y' = 2x O D B.

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Q: Find the general solution, given that y₁ = e satisfies the complementary equation. Use c₁ and ₂ for…

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Q: Find the general solution Y" + 4y² + 2y = ex

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Q: + 5 , ydt + 2y = 10 with y(0) = 0 dt

A: For finding the solution of given differential equation we apply Laplace transform method.