Let the following higher order differential equation y" – 2 y" – 3 y' = 3e5z (1). Determine the general solution of (1) using variation of parameters method for particular solution yp.

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Q: The dependent variable y is missing in the given differential equation. Proceed as in Example 1 and…

A: Given that        y''+y'2+4=0‐‐‐‐1        we have to solve this using the substitution        u=y'

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

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A: The differential equation is x2(dy/dx) + x ( x + 2) y =ex.

Q: 1 3. y' -- %3D xy+x²y3

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Q: 2. y-폼-y 1 ミ、 6x 3x2 ||

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Q: Excrcise 1: 1. Let the following higher order differential equation (1) y/" – 2 y" – 3 y = 3e.…

A: For higher order differential equation,           Let  P0xyn +P1xyn-1+.........+Pnxy =F(x) .....(A)…

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Q: y' - Зу %3D =x*y/3

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Q: The particular solution of the following nonhomogeneous differential equation y" – 2y' + y = 4x² +…

A: y''-2y'+y=4x2+ex This has characteristic equation               λ2-2λ+1=0λ-12=0λ=1…

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Q: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

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Q: 2. Solve the first order linear differential equation y'+2xy = x, with initial value y(0) =1.

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Q: 4. The Bernoulli's form of the differential equation x²dy + (2xy-y³)dx=0 is

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