Use these fundamental solutions, e-2x and e-4x, to solve the initial value problem yII+6yI+8y=0 y(0)=7, yI(0)=-1

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: personal income that is used to pay pers given by y = 0.034x2 – 0.044x + 12.64 where x is the number…

A: The percentage of total income that is used to pay personal taxes is given by,…

Q: x1 = X2 = Solve the following initial value problem: d 15 4 4et ²-(4 15 ) ² + ( 16 ) = dt 64 -16et…

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Q: (2) Solve for y in terms of x In (2y+1) + 3x = 1n (4) -1 given

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Q: Solve an = an-1 +3n² – 3n+1 with A, = 0

A: We will find the solution of given recurrence equation by rearranging terms on the non homogeneous…

Q: Solve the equation In (x + 2) + In (x – 1) = In (9x – 17) and check your answers (True / False) %3D

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Q: First Order Bernoulli DE B.y + y = xy², y(0) = +

A: The given differential equation is y'+y=xy2, y(0)=1/4.

Q: Solve the difference equation: 3 (²7) y[n+ 2] - n> 0 y[0] = 10 and Y y[n + 1] + y[1] = 4 n (1) ₁…

A: Given difference equation is ,      yn+2-32yn+1+12yn = 14n   ;  n≥0     ;  y[0]=10  and  y[1]=4 (.)…

Q: Solve the difference equation In+2 + In+1 – 2.x, = 0 subject to the initial conditions ro = 1 and r…

A: To find- Solve the difference equation xn+2 + xn+1 - 2xn = 0 subject to initial conditions x0 = 1…

Q: If the general solution of (2+²-3y2) y'= 2xyżsy"In|y"+xª = Cy", what is the value of b? (A) 3 B 2 -1…

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Q: 2. Solve the initial value problem x1 = x2, x2 = -x1-2x2 + 4e, x1(0) = 1, x2(0) = 0.

A: Given question are from simultaneous differential equation so we solve it from the concept of…

Q: Solve 1 0-²40 = 5 x (0) = - 4, y(0) = 10

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Q: 1) Find the general solution of the equation x³y"" - 2x2y" - 4xy' + 8y = x² + lnx.

A: In this question we will find the general solution of the differential equations.

Q: Solve y+y = 1, y (0) = 4 Oy² = 1 +7e-² Oy = 1+7e-² Oy² = 1 +7e-² Oy = 1+5e-² Oy = 1+7e²

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Q: Find all the solutions to 4x+1=(12x+3)e* -

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Q: x₁ = x2 = X3 Solve the following initial value problem: -4 1 +6:9--0 = -3 -8 -2 , (0) = -1 -1 -11,…

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Q: (i) Find the solution set of the following equations: 2log, x- 3log, y =7 and log, x-21log, y = 4

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

Q: dy-5+4y =16x+20e" dx ; y(0) = 0, y'(0) =1 dx

A: Given differential equation d2ydx2-5dydx+4y=16x+20ex. The Auxiliary equation is…

Q: Differential Equations. 100 150 Very large tank initially contains of Salt Water Containing gallons…

A: As per the guidelines I did first question.

Q: du 17. t = t² + 3u, t> 0, u(2) = 4 dt

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Q: 1. Solve the following initial value problem: 11x₁(t) +-6x2(t) = x₁(t) 20x1 (t) - 112(t) = x₂(t)…

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Q: suonenba 5x mons: (1) +- = 3x + 3 (ii) x + 7x + 12 = 0 In (x +4)- In (x*) = 4 = 15 (iii) %3D (iv)…

A: Simplification

Q: I. Solve for the unknown/s. 1. x:4 = (2x + 3) = 12 2. (x+ 1): (2x + 3) = (x + 3)(2x + 8) 3. (3x –…

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Q: compute the general solution of the given equation

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Q: Solve 0-240 -5 x(t) = y(t) = x (0) = 8, y(0) = -8

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Q: Example 9.13. Solve Yx+1-yx + xyx+1 Yx = 0 given y₁ = 2.

A: Let us solve the given problem in the next step.

Q: Show that the equation x³ - 3x + 1 = 0 has exactly · 3x + 1 = 0 has exactly one solution in [−1, 1].

A: First we show that given equation has atleast one solution in [-1,1]. Then, by method of…

Q: solve for 1, x = 2x² – 5x + 2, z = - (x+t) - (x) t

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Q: dy (a) dx JE, y(1) = 2 dy (b) dt sin t + 1, y () =; dy (c) dx x +1 y(1) = 0

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Q: (6) Solve y-9y" + 8y = 0.

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Q: Solve the ytem 2x -44 = 6 メ+そツ= ダ+ダそ= /o

A: It's system of equations so I'm providing hand written solution for better understanding.

Q: solve ar + b 35. 2; for x Cx + d - 2[b – 3(c – x)] = 6; for x 37. a'x + (a – 1) = (a + 1)x; for x

A: Since you have posted multiple questions we solved first question for you To get the solution of…

Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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Q: Solve 2 []-[² x(t) = y(t) = 2 -5 -4 X x (0) = 8, y(0) = -10

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