What is an autonomous differential equation? What are its equilibrium values? How do they differ from critical points? What is a stable equilibrium value? Unstable?

Q: Create a differential equations exercise related to Cooling and warming  (Describe the situation)

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Q: find the general solution of the pictorlal differential equation.

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Q: How  can we apply second-order differential equations to the study of vibrating springs and electric…

A: Generally the equations of the analogous systems are second order differential equation with…

Q: What does the general solution of a first-order differential equation represent geometrically?

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Q: The decay is basically governed by the first order differential equation = - ka is

A: We have to identify the given statement as true or false.

Q: What is the general form and standard form of exact differential equations?

A: Differential equation: A equation is that the linear combination of the variable quantity and…

Q: Which is not a form of differential equation is...

A: This is the forms of difference equation and series in summation notation.

Q: Please explain the general process( steps taken)  for solving any nonhomogeneous linear differential…

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Q: Explain the properties of ordinary differential equations.

A: We have to solve

Q: Sketch the phase lines for the given differential equation. Identify the equilibrium points as…

A: As per the guideline i am anwsering the first question only.(Since second question is independent of…

Q: What are the rules or theorems that you may use to identify the difference between linear and…

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Q: What are modeled with differential equations?

A: Here we define the differential equations.

Q: Determine the critical value for Differential Equation

A: For finding the critical value, equate the differential equation to zero.

Q: A car traveling at 100 km/h skids 50 m after its brakes are suddenly applied. Set up a differential…

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Q: Based on a function, try to construct a non-homogenous differential equation with at least 2nd order…

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Q: What is a first-order linear differential equation?

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

A: Differentiating the given genaral solution we can verify if the solution satisfies the differential…

Q: The general solution of a reduced differential equation is referred to as the: A) singular solution…

A: The general solution of a reduced differential equation is referred as the:-

Q: Explain the Linear Differential Equation?

A: Linear differential equation is linear polynomial equation which consists of derivative of dependent…

Q: True or False. Is this equation a linear differential equation of order one?

A: Given, Differentrial equation

Q: Which are the differential equations and initial conditions?

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Q: Discuss a real time application of linear differential equation

A: According to the given information, it is required to explain about the real time application of…

Q: Differential equation, please reply as soon as possible

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Q: Find the critical points and sketch the phase portrait of the given autonomous first order…

A: Consider the provided autonomous first order differential equation.

Q: A solution which contains as many as arbitrary constants as the order of differential equation is…

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Q: Define a differential equation.

A: A differential equation is an equation containing the independent variable x, the dependent variable…

Q: What is an autonomous system of differential equations? What is a solution to such a system? What is…

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Q: Choose the best option that describes this differential equation i) separable ii) linear iii) both…

A: Given differential equation y'=xy+xe-x2

Q: Can a nonlinear differential equation be separable? If so, give an example.

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Q: A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing…

A: A tank initially contains 100 gallon of brine with 40lb of dissolved salt. A brine containing…

Q: a partial differential equation can have more than one independent variable. true or false?

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Q: What does the term “first-order” refer to in a first-order linear differential equation?

A: The term "first-order" means that the highest derivative present in the given differential equation…

Q: Define linear differential equation

A: Linear Differential Equation is an equation having a variable and a derivative of this variable and…

Q: Explain in detail the use of partial differential equations in the application of heat transfer

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Q: What is a Solution to an Ordinary Differential Equations?

A: The Solution to an Ordinary Differential Equation is an equation that satisfies the given…

Q: Can you provide atleast 5 average or complex examples of Ordinary Differential Equations?

A: I listed 5 example of ODE with answers.

Q: Find the equilibrium point(s) for the differential equation y" =y - y2 and determine their stability

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Q: What is the difference between a first-order linear differential equation and a second-order linear…

A: We can explain the answer as below.

Q: After a correct transformation of variable, a homogeneous differential equation will be reduced to a…

A: We have to check given statement true or false

Q: ди ди following partial differential equation = дх at

A: Given,      ∂u∂x=∂u∂t-u                     ...(1)

Q: Create a differential equations exercise related to heating and cooling. (Describe the situation)

A: The given problem is to create the differential equation which is related to heating and cooling, we…

Q: Take a problem statement of your own choice and make its mathematical form as a partial differential…

A: Take a problem statement of your own choice and make its mathematical form as a partial differential…

Q: What does it mean for a function to be a solution to a differential equation?

A: A function is said to be a solution of differential equation if it satisfies the differential…

Q: Use linearization to classify the fixed point for the differential equation i = e -1.

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Q: Write a differential equation showing the family of lines with slope and y-intercept equal

A: Equation of lines is y=mx +c ; where 'm' is the slope and 'c' is the y-intercept.

Q: Explain numerical approximation of solutions of systems of differentialequations?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.