(e) x = 4 – z2 - (f) x² – y² + 4y + z² + 2z = 0

Q: E R -2x - 6 M NL = %3D 2x – 14 SR = I+ 15 x+2 wV = x+21 F FD WN = 4y x + 4 6(y -1) 4x -2

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Q: Find the 2nd solution by reduction of order. y" - 4y + 4y=0; y₁ = e²x

A: Here given the differential equation as y''-4y'+4y=0 .......(1) And it's one solution is y1=e2x

Q: Is y = e-x + 2xe-* a solution to y" + 2y' + y = 0.

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Q: y′′ + 2y′ − 8y = 2e-2x − e−x , y(0) = 1, y′ (0) = 0.

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Q: Find the general solution of: y(x°+x*)dx - x(x³+ y-)dy = 0

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Q: If y = f(x) is the solution of y' – 3y =-12.e 9z, f(0) =1, then

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Q: Find the solution by using Solution of 2nd order D-Es 2 X ý XỨ ty - xy + y = Lnx -

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Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: Obtain the general solution. xy3dx+ex^2dy=0

A: The given differential equation is xy3dx+ex2dy=0. We have to obtain a general solution.

Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: find general solution. dr/dt= -2tr,         r(0)=ro

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Q: dy-Hy-5 te %3D xp

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Q: find the general solution of (y^3 + yz^2 -z)dy + (z^3 + y^2 z - y) dz = 0

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Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: y''-3y'+2y=5e^3x,y1=e^x

A: Reduction of order is a very significant and basic method to solve higher-order linear differential…

Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Resuelva yDx - 2(x+y) Dy=0 O x² + 2y = cy² Ox+2=cy² O x + 2y = cy² Ox+2y=c

A: Given differential equation y D x-2(x+y) D y=0 The objective is to solve the differential equation.

Q: Find general solution of y" – 2y' + y = , By Variation of t2+1' parameter method.

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Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

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Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: Find the general solution using the method of undetermined coefficients. dx +7x=8e° dt -41

A: Answer

Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

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Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

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Q: The general solution of (D³+4D)y=0 is Ay=ex(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁ex+c₂e²x +…

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Q: Let_y=x² +5x³-4x+1 then dy- ||

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Q: 3. Find the general solution of y" – 3y' + 2y = e" using the method of variation of parameters.

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Q: x+3y+z=90     7y+2z=56 Using the echelon method

A: observe that the number of variables is great than the number of equations. So, one of the variables…

Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

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Q: 1l y" + 4y' + 4y = e-2x %3D x2

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Q: Q2. Find general solution of the DE 4y" + 4y" + y' = 0

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Q: dy - Find the general solution of Y +2 = 3x²y² dx A. 1/(xy) = -3(x³/2) + C B. 1/(xy) = -3(x²/2) + C…

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Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: 2. Is y(x) = 2sin3x + 4cos3x a solution of y" +9y = 0? %3D

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Q: Find general solution of the DE 4y′′′ + 4y′′ + y′ = 0

A: The given equation is 4y'''+4y''+y'=0. The characteristic equation of the given differential…

Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

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Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: What is the general solution of xy(xy³ −1)dx + x²(1+xy5)dy=0? (A) 2x5y³-3x²= Cx² B 2x³y5-3x2= Cy²…

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Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

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Q: y = (2x + 1)v2x+1

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Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

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Q: OBTAIN THE GENERAL SOLUTION (x - 1) dx - (3x - 2y - 5) dy = 0

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Q: (D³ + 2D² - 5D - 8)y = 0, when x = 0, y = 0, y = 0, y" = 2

A: Given

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.