Question 15 Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 1 5t 14 -21 (A y(t) 35 10 13 12 -51 _ 13 ,21 10 у (1) 14 35 1 5 13 -21 © y(1) e 10 35 14 1 -Sr _ 13 21 D y(t) = 10 35 14 + B.

Q: 4. y=x+c₁e* + C2e-* y" -y + x = 0

A: Since you have posted multiple question, I can do first question as per our company guidelines.…

Q: c) u' - 6u = 6 d)-1 Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are): c) 0 b) 0,-1 a)…

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Q: Solve the D. E. to the I. V.P. (1 +x² + y² + x?y²)y' = y², 2. y(1) = 1

A: The solution is given as

Q: 4ry" +2y' +y = 0. Solve using Frobenius

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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: 5. z3 – 2iz2 + 4z – 5i = 0 →3u

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Q: 3 2 y' у. -5 1

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Q: Find general solutions 17. y" - 4y = -12r² +6x-4; 18. y"+y+y = -13 sin(2x); 19. yy=e+xz; 20. y" - 4y…

A: 19)  We have given a differential equation ,  y'' - y = ex + x First we will find complementary…

Q: Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c) s²L(y(x))-sy(0) - y'(0) b) s²L(y(x)) + sy(0) + y'(0) d)…

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Q: 5-    y" + 8y' + 16y = 0   7-  12y"− 5y'− 2y = 0

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Q: answer each question by true or false and explain 1) L{t * e³t} = L{te³t} 2) L-¹{L{t* et}} = t * e³t

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Q: Find the general solution of the following Cauchy-Euler equation x²y" - 2xy' - 2y = 0

A: We have to find the general solution of

Q: An auditorium has 28 rows of seats. There are n=24 seats in the first row, 25 seats in the second…

A: Given that an auditorium has 28 rows.  Number seats in first row= 24  Number seats in second row= 25…

Q: x' - x? = t, x(0) = -2, 0, 2; x(2) = 0; x(2.5) = -3, 0, 3 7. y'= sin(yx), y(0) = 0.5, 1,1.5, 2, 2.5…

A: We will use Mathematica to solve these. Each question has multiple initial value problems. 6 (a):…

Q: 5. sin x cos? y dx + cos? x dy = 0

A: As per the guidelines, we are suppose to answer only one question. Please repost the rest of the…

Q: 3) L-1{}.} } = L {{}L'{}

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Q: answer each question by true or false and expla 1) L{t * e³t} = L{te³t} 2) L-¹{L{t * et}} = t * e³t

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Q: 1 1 Let A = 1 2 3 and B = (b, b, b3) be the inverse of A. 1 3 4 Which of the following is equal to…

A: Answer

Q: r3 + y = Ty, then y = 32 3» ყ passos " 1 — 34 + ყ 3.72 O x - 3x² + y 3y² O 32 — y — 3g2 - lf

A: Given

Q: 5. It is given that two linearly independent solutions of x²y + xy + - y=0, x>0 are -1/2 sina and…

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Q: You plan to buy a car at purchase price $P with no down payment. You have a choice between 0% dealer…

A: Here, dealer financing is preferable.

Q: Use undetermined coefficients to find the particular solution to y"-2y+4y= 4t+7 Yp(t) =

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Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as

Q: 2. y" - 3y' +2y = e4x + 6x3 – 2+ 3sin(4x)

A: The given differential equation is  y" - 3y' +2y = e4x + 6x3 - 2 + 3sin(4x)

Q: e general solution to y" - y' + (81x¹ −72) y = 0. X

A: Given    y''-5xy'+81x4-72x2y=0  Here we use the formulas:  to find Integrating Factor(I.F)=e∫P(x)dx…