A linear differential equation of the first order can be written in the following form, which is called the standard form: see picture 1 To solve this equation, a function {\ displaystyle m (x)} m (x) is determined, which is such that if the equation is multiplied by this, then the left-hand side becomes the derivative of the product  m (x) y. The function  m (x) is called the integrating factor, and is determined by see picture 2

Q: Consider the differential equation ay" + by' + cy = 0, with a, b, c ЄR and a 0. Given that the…

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Q: čônčěntrátion enters the tank at 20 kg/min and the mixture leaves the tank after complete mixing at…

A: Given Mass=1000 kg of a 10% salt solution Tinput=2okg/minute→2o% concentration Toutput=1okg/minute…

Q: : xydx - (x + 2y)2 dy = 0

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Q: dy +y: da 20

A: The value of n is -2

Q: y = -CI cos 3x + C2sin 3X

A: Given, y=c1cos3x+c2sin3x We have to find the corresponding differential equation by elimination of…

Q: (y - 3y + 2)√9+ x²dx + x²dy = 0

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Q: If the differential equation: (y5 + kx²y¹ + 3x)dx + (5xy¹ + 16x³y³ – 4y)dy = 0 is exact, find the…

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Q: 3 tanx-2xy = c

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Q: Find the general solution of the given differential equation. y'''-3y''+3y'-y=0 If using a…

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Q: equation

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Q: xy2y' = x + 1.

A: answer is in step 2

Q: Solve the Linear Higher Order of differential equation using the formulas below. (D³ – 2D² +…

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

Q: Consider the differential equation -3 y' - ycos²(x) = (a) Sketch the direction field for this…

A: The direction field is the collection of small line segments passing through various points that are…

Q: ind m so that y =emr is a solution of the differential equation y'=-9y.

A: Take y=emx be the solution, then it must satisfy the given ode.

Q: Q2: Solve the High order differential equation by using Operator Method y(4) – 6y"" 5x

A: We have to solve the given problem by operator method.

Q: C) The dependent variable y is missing in the given differential equation. Solve the equation by…

A: To solve the given differential education.

Q: Solve the given differential equation. x?y" - 12y = 0 +V7 Y(x) =

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Q: 2xy 9x² + (2y + x² + 1)dydx = 0

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Q: . Find a general solution of the differential equation y" 2y3y=3x²–5

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Q: 4) (e* + y)dx + (2y + x)dy = 0

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Q: Joanna is investigating how a harmful substance from pollution is absorbed by the human body. She…

A: To find the general solution to the given system of the differential equation.…

Q: dv/du = (u - v)² -2(u - v) - 2.

A: Given differential equation is,To Find: solution of given differential equation by using Bernoilli's…

Q: Solve the differential equation: y''+4y = 0

A: Solve the differential equation: y''+4y = 0

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.