4.Determine if the given function is a solution of the given differential equation

Q: Obtain the differential equation associated with the given function: y = Cx² + c2.

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Q: 2) хду + ху 3 е* + 1 %3D

A: Given differential equation x3y'+xy=ex+1. The main objective is to find the general/particular…

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

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Q: Question The solution of the following homogenous differential equation: y(5) + y(3) 0 is:

A: Explanation of the answer is as follows

Q: Find general solution for the following linear differential equation: y' + 2ty = 4t.

A: Given that: y'+2ty=4t

Q: In the given question , determine whether the function is a solution of the differential equation…

A: Definition of the solution of the differential equation helps to determine whether the given…

Q: 5. Solve the given partial differential equation ôx

A: Need to find C.F only

Q: Determine whether the following equation is a solution to the corresponding differential equation.

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Q: Determine the general solution of the differential equation xdy+ydx=2x^2ydx

A: Given differential equation is xdy+ydx=2x2ydx. We have to find the general solution of the given…

Q: Determine if the function is a solution to the given differential equation. y = x In x + 6x + 5; y"…

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Q: x +y = x³ /y X-

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Q: 8.) y Inxlny dx + dy = 0

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: In the given question , determine whether the function is a solution of the differential equation…

A: Substitute the value of y in the equation to determine whether the function is a solution to it or…

Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

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

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

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-2t 2 = 0

A: We need to determine a differential equation corresponding to the general solution: y=c1e5t+c2e-2t.

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

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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. Solve the following linear differential equations with constant coefficients:

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find a particular solution to the differential equation y" + Oz/ – 16y = -768t°.

A: Given: y'' + 0y' - 16y = -768t3

Q: Which of the following is the general solution to the differential equation?

A: In this question, we find the general solution of differential equations by using given…

Q: In the given question , determine whether the function is a solution of the differential equation…

A: To Determine: y = 3 cos 2x  is a solution of the differential equation y(4) -16 y= 0.

Q: 3(/)

A: given functiony''+3(y')2+9=0         (1)let y'=v ( v is function of t)then y''=v'therefore  equation…

Q: y= 4 + Inx; xy'

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

Q: 13.Find a differential equation whose general solution is y = c1e2t + c2e−3t.

A: The given solution is y= c1e2t+c2e−3t.

Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: In the given question , determine whether the statement is true or false. If it is false, explain…

A: If y=fx is a solution of a first-order differential equation, then y=fx+C is also a solution. The…

Q: 1. Evaluate the solution for the following differential equation

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Q: y=ae³x + be-3; y"-9y=0 -3.x.

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Q: b) Find the general solution to the differential equation

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

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Q: In the given question , determine whether the function is a solution of the differential equation…

A: The given differential equation is y(4)-16y=0y=3 sin 2x

Q: find the degree of the differential equation y''-12cosec y= 0   3 1 4 or 2

A: The order of the differential equation is 2.

Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. 2y' + 3y =…

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Q: ;C, C2 and Cz åré årbi

A: y=c1e10x+c2e-9x+c3e8x; c1,c2,c3 are arbitrary constant.ddx(emx)=emxm+cIf we differentiate two times…

Q: Find the solution of the following differential equation.

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Q: Find the general solution of the following differential equation.

A: Here the differential equation is homogeneous so only complementary function is the final solution.

Q: Find a differential equation whose general solution is y = cje% + cze¯74. = 0

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Q: Find the general explicit solution to the differential equation y′ − 3x2y = x2

A: The given differential equation is y'-3x2y =x2. We solve the differential equation by separation of…

Q: а. у %3D Ае2х + Вхе2x

A: We eliminate A and B by taking first derivative y' and second derivative y''

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: Verify that the given function is a solution to the given differential equation у — x3 solves y' =…

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Q: Obtain the solution on the following differential equations:

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Q: 4. If y, (1) = a is a solution of dy dr Find the second linear independent solution and the general…

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Q: 4. Verify that the function y = is an (4 – 12) explicit solution of the differential equation y' =…

A: To veryfy that the function y=14-x2 is an explict solution of the differential equation, y'=2xy2.

Q: Obtain the differential equation associated with the given function: y = Cx² + C².

A: first we will derivative with restive x then find the value of C then put in given equation

Q: find the general solution of the following differential equation if one solution is known to be y=x…

A: Using the reduction of order

Q: Which of the following is the differential equation that accepts the solution as the family of…

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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.