PLEASE ANSWER THE FOLLOWING POINTS: E) IVP'S AND ALL FROM VARATION OF PARAMETERS   y´´ - 4y´ = 6e^3x - 3e^-x y(0)=1 y´(0)=-1 e)  Use the IVP’s to find the particular solution f)  Solve the differential equation by VARIATION OF PARAMETERS g)  Report the Wronskian ?

Q: Q1: When to use each rule for solving differential equation in order to change the differential…

A: When the differential equation consists of more than one variable in order to keep one variable…

Q: Find the differential of the function. y = e³x dy = =

A: We have given function  y=e3x dydx=ddxe3x dydx=e3x·ddx3x dydx=e3x·3 dydx=3e3x dy=3e3x dx

Q: Q. Find general Solution of the differential equation

A: We need to solve t2y''+3ty'-3y=t-1 We use Cauchy Euler equation to solve this: Let t=ez  ⇒z=logt…

Q: TSolve the boundary value problem (D² + 9)y = sin² x given that y(0) = 0, y () = 0 T 6.

A:

Q: Is the following a homogenous differential equation? dy/dx = (x2y-y2x)/(x3-y3)

A: Let's find

Q: dy +y: da 20

A: The value of n is -2

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Q: - Solve the differential equation: y" + y = secxtanx

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Q: Find the differential equation of the following families of curves: y2(b+x)=x2(3b-x)

A: Given y2(b+x) = x2(3b-x)                 (1) Differentiate equation (1) with respect to x , we get…

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Q: y" + 3y=-48x²e³x

A: Differential equation and it's solution

Q: The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

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: 8. Given two events X and Y: Event X has probability. If event X happens, then the probability of…

A:

Q: Solve the following Clairaut equation   y=xy'+(y')^2

A: Firstly we will differentiate this equation to get simpler differential equation

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Q: Find the differential equation of all circles passing through the origin and having their centers on…

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

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Q: Show that y=x and yex are lenean inde pendent Solution of the Corres pondinp hamogeneous part ot the…

A:

Q: (d) Determine the (i) critical points of Eq. (3). (ii) limiting and threshold solutions from Eq.…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find the differential equation of all circles passing through the origin and having their centers on…

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Q: V34

A:

Q: Construct a table of similarities and differences for Legendre, Laguerre and Hermite differential…

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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.