2. Which of the following represents all solutions of x -4x -1=0? (1) 2± 5 (3) 2±V10 (2) –2+ 5 (4) –2±V12

Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general solution. A…

A: Given Differential equation is x'' - 4x' + 4x = 4e2t

Q: 11. Find the particular solution of 2ydx = 3xdy, when x -2, y = 1

A: Given : Differential equation :  2ydx = 3xdy And x = -2, y = 1   To find : Particular solution of…

Q: 5. Eliminate the arbitrary constant on the given equation: -4xy2 + xy. C

A:

Q: 5. Find a general solution to the Cauchy-Euler equation x?y" + 7xy' + 9y = 0, for x > 0.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Find the general solution of the following DE. xy(y')² + (x² + y²)y' + xy = 0

A: Here given the differential equation as xyy'2+x2+y2y'+xy=0 Replace y' by p, then xyp2+x2+y2p+xy=0…

Q: Find the general solution of the following DE in explicit form. y'=2+2y-2x +8

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: What is the general solution of (1 + x²) y = x*y 3ry + 1= C 3xy + 3y tan e 1. 3ry 3y tan 3ry + 3y…

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Q: Find the general solution of i = Ax, where A = .

A:

Q: Find a particular solution of (8) y′′′−4y′=t+3cost+e−2t.

A:

Q: Solve the following. IP 101 dt 2t +5 = 10, I(0)=0 = 2X 1. +3y dr ; r=1, 0=1 4. ydx+(3+3x-y)dy=o 2.…

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Q: What is the particular solution for y′=6e^x+x^2−7x such that y(0)=6?

A: Given problem:- y'= 6ex+x2-7x  Particular solution for given differential equation when y(0) =6

Q: Find the general solution of the differencial : (o²-9)y equatión ex + Sin 3x

A: To find the general solution of the differential equation

Q: 5. Eliminate the arbitrary constant on the given equation: -4xy + xy2 = C

A:

Q: Solve the following using variable separable. (y’)2 =  1 − y2/1 − x2         ;         y = 1/2, x…

A:

Q: 1. Determine the following: 8. S(V)° -+ - 9 7 dx (4x-1)3. 2-x 2x5-4Vx+3 h. S

A:

Q: 8. Solve the following LP algebraically. a. Max Z= 150X+ 160Y subject to: X+Y 20 Y>15 X, Y>0

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Q: Use the variation of parameters to find the solution to the IVP. 0 1 et 1 X' (t) = x(t) + ,and X(0)…

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 %3D

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Q: Solve the following equation by Gauss-Seidel Method up to 2 iterations and find the value of z.…

A:

Q: Find the general solution of the following equation valid near the origin: (1+4x²) y¹¹-8y=0…

A: Given: Let us consider the given differential equation, 1+4x2yιι-8y=0

Q: determine by inspection at least two solutions of the given first-order IV . 16. xy-  2y, y(0) …

A:

Q: Find the general solution of: az əz 2, дх ду (1+ /z- x – y)

A: The given equation can be written as: 1+z−x−y∂z∂x+∂z∂y=2dx1+z−x−y=dy1=dz2          ......i

Q: 4. Find a second solution to x²y" – 3.xy/ + 5y = 0, given one solution y1(x) = x² cos (In æ).

A: To find- Find a second solution to x2y'' - 3xy' + 5y = 0, given one solution y1x = x2coslnx.

Q: Find the particular solution determined by the initial condition. P(X) = 2x ° = 3x )= -6 2/5 - 3x:…

A: This belong to initial value problem of differential equation.first we solve the differential…

Q: 6. Find the smallest constantr so that o(x) == x" is a solution to 3z'y" +11lry -3y= 0, for z >0 -3…

A: 6.ϕr=xr is a solution to 3x2y''+11xy'-3y=0, for x>0

Q: Find a particular solution to y′′+16y=24sin(4t).

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Q: y' + 2y = x³e-2x

A:

Q: Solve for the particular solution of the following non-homogeneous DE. y”’ + y” = 3

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Q: For #1-10. Solve for the particular solution of the following non-homogeneous DE. 1. y" + 4y' + 3y =…

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Q: y = 3 (y + 1)

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Q: Use the IVT to show that e−x2 = x has a solution on (0, 1).

A: Given equation is

Q: 24. Find the first approximate solutions for -2x? + 4x + 2 = 0. 1 - and x = 3- 3 3 x = and x = 3- 3…

A: -2x2+4x +2 = 0Dividing Both the Sides by -2x2-2x-1 = 0Since the coefficient of x2 is 1Move the…

Q: 4. Solve the given nonhomogeneous( or undetermined coefficient( O.D.E by variation of parameters (2)…

A: We have the given question,  This is a Euler-Cauchy Differential Equation of the form ax2y''(x) +…

Q: Show that the following DE are Bernouli type and solve: 1. y’ – x = y 2. s’+ 2s/t = s 3 t 4

A:

Q: Find a particular solution to y′′+36y=60sin(6t) yp=

A: The given differential equation is  To calculate the particular integral let us consider If we put…

Q: Find the general solution of the DE: y" + y" – 16y' + 20 = 0.

A:

Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general solution. A…

A: Some of the properties of Laplace…

Q: Solve for the particular solution of the following non-homogeneous DE. y''=4

A: solution of non differential equation

Q: Find a general solution of each reducible second-order differ- ential equation x² y" + 3xy' = 2

A: Given: .....(1) Consider, Then,

Q: You're to find x in the second question. Thanks

A:

Q: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

A:

Q: Find the general solution of the following DE. y' = 3 (y + 1)

A:

Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y = 2 and x = 1

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

Q: The solution of e = -has the form x + i (y + 2nn) where n is an integer. What is the value of x?…

A:

Q: 1 Solve 1 3D7 for z. y. 1-

A: 1x-1y-1z=7

Q: Consider the following IVP: x" + 4x = t+4 ; x(0) = 1, x'(0) = 0 Find the general solution.

A: Explanation of the answer is as follows

Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y 2 and x = 1

A:

Q: 4) Prove that y = x-3/2 is a solution to 4x2y" + 12xy' + 3y = 0.

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Q: Which of the following is a solution of the following equation valid near the origin for x>0? 2x2(1-…

A: There are two solutions , from the given options we choose one of the solutions.