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…

Q: Solve this separable differential equation. y' = e-(2x – 4). 3.

A:

Q: What is the differential equation of the family of circles with their centers on the y – axis and…

A: The given problem is to find the differential equation of the family of circles with centres on…

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

A:

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

A:

Q: (D² – 3D + 2) y = (1+e-*)?

A:

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

A:

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

A:

Q: What is the general solution to the the differential equation3y" - y'- 2y = 10e *?

A:

Q: Find the differential equation having the solution as of the following b. (x – r)? + y? = r²

A:

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

A:

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

A:

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

A:

Q: Find the differential equation having each equation as general solution. m y ==-7

A:

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

A:

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

A:

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: (D3-2D2 – 3D)y = 0

A:

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: Find the differential equation whose general solution is y = A + B e^(- 4x)

A:

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)…

A:

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

A: See the details solution in below

Q: a. y = C,e=x + Cze-2x + x

A:

Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

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

A:

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

A:

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

A:

Q: Find the solution of the following differential equation.

A:

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

A:

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

A: Solve the above differential equations.

Q: dy_ 2x+ y-1 dx 4x+2y-4

A:

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

Q: The Complementary Function of the differential equation - 8 + 15y = e is %3D

A:

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

A:

Q: Find an explicit solution to the differential equation y-y+3 =0.

A:

Q: Obtain the differential equation whose general solution is y = C1 + C2 e^.

A: The given general solution is                y= c1+c2e3x We want to find the corresponding…

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

A:

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 *

A:

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

A:

Q: (Dª – 16D²)y = 0

A: Differential equation: - The generic solution is one that comprises as many arbitrary constants as…

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

A: