What will be the order of the differential equation if its solution is y=Acos7x-Bsin7x a. None of these O b. 2 О с. 3 O d. 1

Q: Find the particular solution for the differential equation y' = 4xe2x and y(0)=20.

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Q: Select the general solution to-the differential equation: y = 3x y 1 y = Vx3 + C y = e3z3 y = Cez 1…

A: Given Differebtial Equation,  y'=3x2y dydx=3x2y

Q: For what value of x will the curve y = x3 – 3x2 + 4 be concave upward?

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Q: a. Classify and solve the first order differential equation y' = /2 +e'.

A: Answer  Linear differential equation is of the form         y'+Py=Q Where P,Q are function of t.

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

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Q: 4. Eliminate the arbitrary constant 'a' in the differential equation: y – 2ay' + x2 = a? %3D

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Q: Find a differential equation whose general solution is y = c₁e³t+c₂e-3t 5t = 0

A: The general solution,y=c1e5t+c2e-3t

Q: What is the general solution of the differential equation of (z + y?) dr + rydy = 0 (22

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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: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A: Given,  In a certain company, the relationship between the price per unit P and the weekly sale y,…

Q: Solve for the general solution of the below differential equation y" + 8y + 25 0

A: Given the differential equation is y''+8y+25=0. Calculate the general solution of the given…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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Q: yi = 3y, + 2y; y - +2y;

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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: Find the particular solution for the differential equation y' 4xe2x and y(0) =20.

A: Given that a differential equation and we find its particular solution . and also given that a…

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

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Q: (y – c,)² + (x – c2)² = 1 %3D -

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Q: Form the differential equation by eliminating the arbitrary constant A, B from y=Ae?x+Be7*

A: We have to form differential equations

Q: 5. Find the general solution of the differential equation. 21xy' + y = 462X

A: What is Ordinary Differential Equation: Solving an ordinary differential equation is an application…

Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

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Q: y = y2 y = Yı)

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Q: Find the differential equation of the family of -2x y = A1eª + A, e 2a

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Q: State the order of the given ordinary differential equation. t8y(6) – tAy" + 7y = 0

A: Order of differential equation is defined as the order of highest derivative in the given…

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

A: Given: y'' + 0y' - 16y = -768t3

Q: What is the solution of the following differential equation that satisfies y (1) = 7 and y '(2) = 3?…

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Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: + tx* + = 0 + tx3 +

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Q: 4y" + y' = 0

A: We calculate differential equation by the help of Euler identity

Q: 1. Obtain the differential equation associated with y=Ax2+Bx+C

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Q: y=ae³x + be-3; y"-9y=0 -3.x.

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Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

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Q: What is the order of the differential equation which has a general solution given by y = Cie-2a +…

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Q: Obtain the general solution of the following higher order differential equation. 4. (64D3 + 27)y = 0

A: Given higher order differential equation, The auxiliary equation will be This will become,

Q: Obtain the general solution of the following higher order differential equation. 3. (D3 + 8D2 - D -…

A: The given higher order differential equation is D3+8D2-D-8y=0

Q: What is the differential equation of 2y'=3y+1 when y(1)=0

A: Consider the provided D.E 2y'=3y+1  when y1=0 We need to find the solution of the given D.E, Since,…

Q: (i+ y? tXy?) dr t (x?y ty +2xy) dy

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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: y = c1 e(-2+v3)x + c» + c2 e(-2-v/3) z

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Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

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Q: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

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Q: 4. (4D2 + 4D + 1)y = 7e-* + 2 when y(0) = 1; y'(0) = 3

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Q: 5) Verify that y = 2e3 – 2x – 2 is a solution to the differential equation y' – 3y = 6x + 4. - -

A: Given that y=2e3x-2x-2    ......(1) Differentiating (1) with respect to x: y'=6e3x-2…

Q: Solve the differential equation. regarding y as the independent variable rather than x. by |26. (1 —…

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Q: y = cje + c2er

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Q: dy 2xy%=D0

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Q: If y = c1e5* + c2xe3* is the general solution of the differential equation y" + ky' + my = 0, then…

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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: Which of the following can NOT be the linearly independent solutions of the differential equation y"…

A: Here 1, x are the solutions of ode. then their linear combinations also solution  but option C can’t…

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: (Dª – 16D²)y = 0

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

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.