5. Consider the ODE y" + ky' + 36y= 2eßt with 3 and k constant. If this ODE has a particular solution given by t²eßt, what is the product of 3 and k?

Q: Dy + Ox D'y )u =0

A: We have to solve given problem:

Q: 1) 9y" – 30y' + 25y = 0 2) y" – 4y' + 3y = 0

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Q: solve the ode

A: Given y"+y'+y=0

Q: Determine the solutions of the following first-order ODEs:  Tip:y'=xv'+v          y=xv *…

A: When a function fx,y can be expressed in the form of ϕyx or ϕxy, the function is referred to as…

Q: Q1: Solve the following ODE a) y" + 2y' - 6y = 0 b) y'"- 6y" +12y' - 8y = 0 c) y"+y'- 2y = x².

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

Q: Find the solution of the given ODE a. 1 - 2 = Cx b. 1 + (-)² = Cx c. 1 - * = Cx y d. 1 + (-)² = Cx…

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Q: 3. zy if y + x² – 3xz = 222

A:

Q: 9) y= 3sin 0 +2 %3D TC 3T 2

A: y=3sin θ+2

Q: 2.

A:

Q: Find general polutien yoy! + x = 0 of followoing eeparable obts. ODES. a. y' = e*** yz 2メー1 b. = e²

A:

Q: Simplify the following by using De morgan's theorem: (with solution)  1. W = BC +B'C 2. X = A'B +…

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

Q: y'47y'+12y = 2le", y(0)=,0)=-10 .

A:

Q: Find a general solution of the ODE: y" - 2y' +5y=−2+5x+4e* .

A:

Q: 4. Suppose the following functions are a general solution of: y(4) + azy" + azy" + a13 + a0y = 0…

A: The differential equation is y(4) + a3y''' + a2y'' + a1y' + a0y = 0 We have to find a0, a1, a2 and…

Q: 名7 Find fen(x)if fx)=ュ-ズ 2-X

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Q: 7.Find a²z of z = 2x³-5xy² xy

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Q: 7.2. +4 7.2. 1- 'y'+ 16

A: Using integration formula,

Q: Set X = x 0 1 Y where x, y are unkonwns. Solve the equation X² = 10

A: given and

Q: 1 y" + 3y' - 18y = 0 2 y"-14y' +49y = 0 y" + 2y' +10y = 0 y"" — 7y — бу = 0 3

A:

Q: Select all the points through which a unique solution for the DE y'=/13-x²-y2 is guaranteed by the…

A:

Q: 5. (BH) Calculate det B, where 0. 4 1 1 В — 1 -2 4 -1 2 1 -1 0 7

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Q: 1. Do not use a theorem to find the ff. Z if yz? + z = 5xy – 1. %3D

A: In the multivariable function, if we have to find the partial derivative of one variable with…

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: 6. Find a line parallel to 3x - 2y = - 4 and passes through (4,-2)

A: We know if lines are parallel then slopes are equal  Given line equation is 3x-2y=-4

Q: y' – 2y = 3e'

A:

Q: 10 12 Find ¹0¹²(x + In y) dydx

A: Introduction: The surface area of a 2D figure may be determined primarily using the double integral,…

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0.

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Q: Find the complete solution of dy + ydæ = 2ry e" da 01= ye" (C- z) 01=yle(C-') O1= ye" (C + z*)…

A: we have to find the solution of  given differential equation.

Q: 4.2. Suppose that v = (2, 1) and w = (1, 2). (a) What is 3v + w? (b) For c,d e R, what is cv + dw?

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Q: A particular solution of the ODE y8) +2y"-3y'+y=e is def ined by y =e' O Y。ミx? ーr y =x O

A: