Find a solution to the initial value problem, y = 4 y" + 18x = 0, y(0) = −4, y'(0) = 3.

Q: y''-2y'-y=8e^t    find the particular solution

A: In this question we will find the solution of the differential equations.

Q: Solve 2y'' - 5y' - 25y = 0, y(0) = 0, y’(0) = = y(t) = - 37.5

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Q: Solve y" +5y' = (2x+1)e" -5x

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Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

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Q: y = (x + y – 1)².

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Q: Solve: y(4) + 18y"+81y = 0 y(0) = -4, y'(0) = 11, y"(0) = 60, y"(0) = -81

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Q: y' = 3x²+y² xy ; given that y(1) = 1 ; solve for y when x = 2

A: The given equation is; y'=(3x2+y2)/xy, y(1)=1.

Q: Solve xyy'=1+y^2, for y=3 when x=1, or y(1)=3

A: The given differential equation with initial condition is: xyy'=1+y2 where y1=3.…

Q: Solve y'' + y' — 6y = 0, y(0) = 8, y'(0) y(t) = = - 9

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Q: Solve 16y" – 8y" + y' = 0

A: Write the auxiliary equation first and find it's roots.

Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: The general solution of y' = X У can be written in the form = C

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Q: y' = 2x + 2C₁e2x + 3C₂e³x

A: Formation of Differential Equation: When we seek solution to a differential equation, the general…

Q: solve by bernoulli y' + (8/x)y = x6y4

A: We will find out the required general solution for given Bernoulli's equation.

Q: Solve y' = (y − 1)(y + 1) for y(0) = 3.

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Q: QUESTION 6 Let fo(x) = nx2 +5 for neN and x ER 4n +3 1. Show that (f.(x)) converges uniformly on [ -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Equation in (a) becomes the non-homogenous equation, y'' − 2y' +y = e^2x . Solve the particular…

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Q: y' = (4x + y)?

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Q: Solve y"" - 2y' + y = 0

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Q: 5. Solve 2y" - 3y' - 2y = 0; y(0) = 1, y'(0) = -1.

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Q: x+1 Solve y'=- y +1

A: Differential equation

Q: Use the particular solution method to solve y - y = 2e²

A: Given that  a first order linear differential equations and we find particular solution of this…

Q: 3. (ey + 1)²e-dx + (ex + 1)³e¯*dy = 0

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