a. Determine the equation of the family of parabolas whose axis is parallel to the x-axis and whose vertex is on the y-axis. b. Find the differential equation whose solution is the family of parabolas described in part (a).

Q: Find the differential equation whose solutions correspond to the following equation 1. y = C,e¬* +…

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: Find the differential equation whose solutions correspond to the following equation 1. y = C1e¬* +…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: b What is the general solution of the differential equation? Reason out why it is the general…

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Q: Show that the given equation is a solution to the differential equation written oppos 1) y = e*( x +…

A: given differential equationy'-y=exthen we have to show that y=ex(x+C)be the solution of given…

Q: Give the degree of the following differential equation  y' - y^2 + y^{(3)} =0

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Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. y' = y2 y =…

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Q: 1- Find the order and the degree of the following differential equation -

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Q: If the differential equation ydx+xdy= 0 is being solved, what is the geometrical figure represented…

A: Differential equations

Q: 2) Find the general solution of the following differential equation

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Q: b. 6y²dx – x(2x³ + y)dy = 0 -

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Q: Show that the given function is a solution to the differential equation y=3x2+1, 2ydx-xdy=2dx

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Q: The general solution of the second-order differential equation y"+y' - 12y = 0 is:

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Q: 4. Identify whether y' - 3y = 6 is a linear differential equation or a Bernoulli equation, and solve…

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Q: The order and degree of the differential equation representing the family of parabolas y = 4a(x-h)…

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Q: 3. Show COMPLETELY that the equation y = C (-1)"x" n=1 is the general solution to the differential…

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Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. y' = y2 y =…

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Q: Find the solution of the following Second Order Differential Equations. y" - 9y = 0,

A: find the solution of the following second order differential equations y''-9y=0

Q: The general solution of the second-order differential equation y"-y'- 12y = 0 is:

A: given differential equation y''-y'-12y=0 lets solve using auxiliary equation

Q: c) y' = -y2e* d) y' = y2 - 4

A: Use the variable separable method to solve.

Q: The order and degree of the differential equation representing the family of parabolas y² = 4a(x-h)…

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Q: Find the roots of the differential equation: y" +4y' +6y= 0

A: See the details solution in below

Q: Show that if the roots of the auxiliary equation of a differential equation are r = p± qi, then the…

A: The given roots are r=p±qi. Show that the differential equation itself is y''-2py'+p2+q2y=0. Here we…

Q: 2 -1 et x + x' %3D 3 -2

A: The given differential equation can be written as:x'=2−13−2x+ett    and…

Q: This is a second order differential equation, Give the complementary solution? xy"-2xy+2y = 2xe

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Q: у' %3D2(2х — у),х %3D0, у %3D 1 || ||

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Q: What is the general solution of the differential equation 2y"+y'-6y=0?

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Q: The complete solution to the nonhomogeneous differential equation (D^3 + D - 10)y = 116e^(4x), is *

A: Explanation of the answer is as follows

Q: Find the solution of the following differential equation.

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Q: 1.3x – xy = c -

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Q: Find the general solution of the following differential equation: (x^2 + 1)у' + 6ху -х

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Q: Find the solution to the differential equation y'-2ty = 4t

A: Solve the above differential equations.

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Q: Find the general solution of the differential equation y′ = 1/ x√(4x2 − 9)

A: To find the general solution of the differential equation y'=1x4x2-9

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Q: 2-Find the general solution of the Differential Equation (2² + 4) y' = 2xy.

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Q: Find the general solution of the given second-order differential equation. у" + бу' + 9у %3D0 y(x) =

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Q: Find the differential equation whose solutions correspond to the following equation a. cx2 + x + y2…

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Q: Solve the following Higher order Differential Equation y(4)- y"+2y-0

A: The general solution of a higher order differential equation is given by;…

Q: The complete solution to the nonhomogeneous differential equation, (D^2 +D - 6)y = 2x, is *

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Q: A/ find solution for the differential equation below: Y"' - 6Y" + 11Y – 6 = 0

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Q: (b) Discuss the complete solution of the differential equation y" + 9y = -5x² + 4cos2x

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Q: (Dª – 16D²)y = 0

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Q: What is the general solution to the the differential equation 3y''-y' - 2y=0? (2/2)

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