10et --2 Use lap lay trensform system dy, to find the solution of the 1 dx -24, + Y3 +Y2 XP

Q: Q-2). Given that y = x' is a solution of 2x*у"+ ху'—3у%3D0, х>0 find a linearly independent solution…

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Q: dP 5. = P- p2 cet Ans: %3D %3D dt 1-P

A: topic - differential  equation

Q: 4-у2 r2x+y dzdædy -V4-y2 Jo

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

A: Follow the steps below to solve a differential equation by the variable separation method. First,…

Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

Q: Find the solution. (D3 +7D2 + 19D + 13)y =0; when x =0, y=0, y' =2, y"=-12 (A y = e*cosx B y =…

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Q: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

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: xp dt of dy A particular solution X, where XeC1 -2t dt Select the correct answer.

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Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: 1 Oy' = %3D xsiny+2sin2y

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Q: Given that d²y 2. +y =0. dx2 Show that y = x is not Solution a

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Q: Obtain the particular solution 1. (D³ +6D² + 12D + 8)y=0 when x = 0, y = 1, y'= -2, y" = 2 2. y" +…

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Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: Q5) Solve the system dx +y = et dt dy dt

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Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

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Q: Obtain the general solution unless otherwise instructed d²y 1. dx2 - y = 10sin²x

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Find the solution. d3x d?x dx – 2–=0 dt + dt3 di2 -21 ® y = c,+c,e'+c,e- -31 D y = c,++ce+c,e-2

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Q: (S+2) (s?+u] solve by using partial straction

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Q: dy 15 +4y-042

A: ∫115+4y-4y2dy

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: Solve using D-Operator 3. y + 2y + y = x²

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Q: SOLVE THE EQUATION (y -2) dx - (x-y-Ddy = o ISSING THE DE LINEAR IN x 4 Y VAKIABLES.

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Q: a) (x² + y² + z²)² = xyz %3D

A: see the attachments below

Q: Find the solution. (D4 + 18D2 + 81)y = 0 A y = (c, + c,x)e²"cos3x + (c,+cx)e2'sin3x. y = (c, + c,)…

A: 16 Given differential equation is D4+18D2+81y=0 We have to find the general solution of the given…

Q: in yy = 2 y-x; %3D

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Q: find the genral solution (D +2D,D, -2D, +2)u = 0

A: Given  Dx2+2DxDy-2Dy+2u=0   …………………(1) Consider the equation F(Dx,Dy)u=0 Here F(Dx,Dy) =…

Q: Solve for the particular solution: dy + 를y3D -2°y"; y(-1) %3D2 dz

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Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: y" (E) + 2y, Ct) -4y, Ct)= 0 C)+y, (t) -3y, CE) = 2 Solve using the resoluh'on by eliminah'on

A: For the solution follow the next steps.

Q: Solve for the particular solution: dy = y + Vr2 – y?, y(2) = 0 %3D - da

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Q: Use Midpoint method dy dr 1 1 reš - 2y, 0<r <1, y(0) = 0 with step size h = 0.5 and the actual…

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Q: Find the solution. (D³ +7D2 + 19D + 13)y =0; when x =0, y=0. y' =2, y"=-12 A y = e-2'sin3x B y =…

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Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. y =c,e+ce+c,e²r+c,cosx + c zsinx y =…

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Q: Find the particular solution of an EDE (2xy2 +1)dx + (2x2y-y)dy%3D0 when x-2 and y=-2 Answer:

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Q: * y"-2xy'+uy = 2, yto)=0, yl)=1 =)ytx)=? %3D find the solution using numerical solution

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

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Q: If y(t) is the solution of - 2y = 4, y(0) =1, then y(t)= %3D %3D

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Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

Q: Solve the dff oq dy 3x寸票-5-2 %3D

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Q: Find the general Solution of DES 2x y Y' = x? +2y} %3D

A: SOLUTION-

Q: Consider the IVP: y" + 9y = 40ex ; y(0) = 5, y'(0) = -2. Find the general solution.

A: Use the given differential and initial conditions.

Q: 4. (Dª + 2D³ – 6D² – 16D – 8)y = 0 - - - %3D

A: The given differential equation,     D4+2D3-6D2-16D-8y=0

Q: Find the solution. (D4 + 18D² + 81)y = 0 A y = (c, + cx)e²"cos3x + (c,+cx)e²"sin3x. B y = (c, + cz*)…

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Q: 2 (х + 2y)dx + (у - х)dy %3D 0

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Q: Find the Solution to Homogeneous LinearEquation: (D3-3D2-3D+1)y=0

A: Given equation is D3-3D2-3D+1y=0 find the solution of the given equation.

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

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.