Q1. Solve the following first order ordinary differential equation. 2y' %3D2x? — 6х?у where y(0) %3D 1

Q: For the following differential equation, (3D - 3D2 - 3D+ 6) y= 0. how many arbitrary constants are…

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Q: Find the complete solution for the following ordinary differential equation y" - y' - 2y = x²

A: Sol

Q: Q3) Solve the following differential equation using finite difference method xy" = y + 5xe-x Using…

A: Given,          xy''=y+5xe-x                                      ...(1) and  0≤x≤1, h=0.25, y(0)=0,…

Q: 3. Select the correct type for the following differential equation (10 Puan) (2xy + 3y²) – (2xy +…

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Q: Solve the following differential equation by variation of parameters method: ỹ-2 y+ y- 1+ x

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Q: Q2-A) Solve the following differential equation using separablemethod. dy 3x + 4x-4 2y - 4 dx

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

A: Given that: y'+2ty=4t

Q: 4. Solve the following Inhomogeneous Differential Equation 1 3/" – y/ + y = 3+e#/2

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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: For the nonhomogeneous linear differential equation of 2nd order, solve the following y" - 4y – 12y…

A: To solve the given 2nd order homogeneous linear differential equation.

Q: Q1- Find one of the solutions of the following ordinary differential equation: 4x2. y" + 4x y' + (x…

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Q: 4. y = Cie+ C2e + Cse, where y(0) =0, y'(0) = 1, y"(0) = 2 %3D

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Q: Which of the following is NOT a possible solution of the differential equation y' + 4y' = 0?

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Q: Solve the following differential equation using Method of Variation in Parameters y" - 2y' + y =…

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Q: 3. Solve the following higher order differential equation given that y() = 0, y'() = 2 [Apply the…

A: Recall: If the root of Auxiliary equation are complex (say) α±iβ then complete solution is…

Q: Solve the following differential equation with initial value = 6x² 2y+cos y y(0) = 0 b) x²y + xy = 1…

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

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Q: Q1- A: Solve the following first order differential equation: y' = x^(2) * y %3D

A: Differential equations of the form y'=f(x)g(y) is called a separable differential equation.…

Q: The solution of the following homogenous differential equation: y(5) + 4y(3) = 0 is:

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Q: Which of the following is a solution to the differential equation y" +9y = 0?

A: Given differential equation is,y''+9y=0Then characteristc equation is,x2+9=0To find solution of…

Q: Solve the following differential equation by using method variation of parameters.    y'' + y' - 6y…

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Q: 3. (D³ – 3D² +4)y = 40cos2x + 6

A: Given, D3-3D2+4y=40 cos2x+6 Its auxiliary equation is, m3-3m2+4=0⇒m+1m-22⇒m=-1,2,2 Hence,…

Q: 5. What is the general solution of the following differential equation ( .6³yod?y =0)? ,d*y +9. dx2…

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Q: What is the general solution of the given differential equation below? y' – 3y = 6

A: In the question we have to find general solution of the differential equation.   NOTE - As per…

Q: 1 1 -y² 4x 1 y' 4x 2xp = 2

A: Givendydx=y24x-y4x-12x,yp=2

Q: Solve the following differential equation on the interval (0, ∞) (in other words, dy y² = x² + y² dx…

A: Solution of given question is written in below steps.

Q: The following differential equation satisfies the following initial condition y(0)=-3. ydy-xdx-0…

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Q: 2. Solve the following homogenous differential equation UTM dy dr - (2² + 3y°) . UTM UTM

A: Given homogenous differential equation- 2xydydx=(x2+3y2) To solve this homogenous differential…

Q: Consider the following quantity, D = 2(x² + y?) By finding its differential equation, show that the…

A: It is given that

Q: 1. Select the correct type for the following differential equation 2ху + 6х + (x2 - 4) у' 3 0 х # +2

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Q: Solve the following initial value problems after showing that the differential equation is exact?…

A: The differential equation of the form Fxdx+Fydy=0 is exact, if it satisfies the condition,…

Q: Solve the following Second Order Differential Equation y''+y = x2 + 1

A: The given differential equation is non-homogeneous second order. Therefore the solution to the…

Q: Solve the following second order nonhomogeneous linear differential equation. y''+4y=0 y(0)=-2…

A: y''+4y=0 find roots r2+4=0 r2=-4 r=±-4 r=±2i r=2i, r=-2i for complex roots general solution is…

Q: Solve the following second order nonhomogeneous linear differential equation. y"-4y'+3y=0 y(0)=0…

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Q: Use Teller's method to solve a differential equation y'=xv/y and when h=0.2 У(1)-2 Use the fifth…

A: Given differential equation is y'=xy with initial condition y(1)=2 Step size is h=0.2 Formula for…

Q: Solve the following Inhomogeneous Differential Equation 1 y" +y' + y = x² – 2x

A: Given differential equation is 14y''+y'+y = x2-2x ⇒ 14D2+D+1 y = x2-2x     where D=ddx and D2=d2dx2

Q: Which of the following is the general solution to the differential equation 4xy -x2-y" dx for x 0?

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Q: y" – 4y' + 13y = e2* cos 3x

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Q: 3 dr- - Art , when: t=0, r=ro 3. dt

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Q: 3. Solve the following higher order differential equation given that y() = 0, y'(품) %3D2 dy + y = 0…

A: The solution is given as

Q: solve the following Second Order Differential Equation  y''+ 4y = 0

A: By using axillary equation

Q: Solve the following differential equation y′′−y = ex by the method of variation of parameters.

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Q: 4. Solve the following Second Order Differential Equation y" +y = r² +1.

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Q: Given y" + (y)° + 5 = 0 is a differential equation with degree 3 and order 5 O TRUE O FALSE

A: Topic = Differential equation FALSE

Q: Solve the following Higher order Differential Equation y(4)- y"+2y-0

A: The general solution of a higher order differential equation is given by;…

Q: Solve the following differential equation with the method of undetermined coefficients y" + y' – 6y…

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Q: y" + 4y = 4sec²2x

A: We have to solve the differential equation