Find the general solution of the following: 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D² – 5D) + 4y = 0 - - (D?

Q: Use the method of reduction of order to find another solution of y"−4y'+4y=0 if y₁=e²x is a solution…

A: The given equation is;  y''-4y'+4y=0 and y1=e2x

Q: Find the Particular solution of the ODE d²y dy - 62-7y = -9e-2x, at y(0) = -2 and ỹ(0) = –13 dx2 dx

A: To find The particular solution of the given ODE.

Q: Find the particular solution of 3x ydx – (x + y)dy = 0 y(1) = -2.

A: 3x2ydx-(x3+y3)dy=0M=3x2yN=-x3-y3My=3x2Nx=-3x2Since My≠NxTherefore, Non Exact diff. eq.Find…

Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

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Q: Find the solution. 2y" - 3y' + y = 0 (A By = c,e 1- ©y = c,e Dy =c,e

A: Find roots of  characteristic  equation  of given differential equation .If roots are real and…

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

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Q: Q5: Find the solution of the following D.Es: 1- x + 5y = x7 at x = +5y 2- y" + 4y + 2y = 13e³x 2, y…

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Q: 2. Find the general solution to d²y dz² dy + 3y = e* dr

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Q: 4. Find the general solution of (x³ + y³) dx = 3xy? dy A. -3x3 + 2y3 Cx B. 7x3 + 2y3 = Cx C. -6x3 -…

A: According to question, Given differential equation, x3 + y3 dx = 3xy2 dy

Q: Find the Particular Solution: y(x-6y)dx-x(2x-9y)dy = 0; when x=1, y=1 a. y²(y+3x) = 3x² * b.…

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Q: The general solution of (D³+4D)y=0 is Ay=e*(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁еx+c₂e²x +…

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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 to t²y" +2ty' - 2y = 0 given that y₁ (t) = t is a solution.

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Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

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Q: What is the general solution of Xy(xy- 1)dx + x²(1+xy)dy=D0? A 4x3y +3x2= Cy 2x y³-3x2= Cx? 2x°y5 -…

A: Option (c) is right Solution...

Q: Find the solution of the D.E. xydx - (x2 + 3y?) dy = 0 Show your solutions on a separate sheet of…

A: Given differential equation is xydx - (x2 + 3y2)dy = 0

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: What is the general solution of xy(xy³ – 1)dx + x²(1+xy)dy= 0 ? A 2x°y3 -3x2= Cx? B 2x³y5-3x² = c ©…

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Q: Find the general solution of (xy² + x²)dy + a. 3xy + y3 = C b. 3xy - y3 = C xydx = 0 с. -Зху - уз с…

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Q: Consider the problem y' =1-2.xy, y(0) = 0 . %3D Find the solution of this D.E.

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

Q: I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D +…

A: Use rules of differential equations

Q: dy dr +y- y²e* 4. Find the general solution of a.ye*(C + x) = 1 b. ye* (С — х) %3 -1 с. уе* (С — х)…

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Q: The general solution of (D3+4D)y=0 js A y= e*(c,cos2x+czsin2x) y=c1+c2cos2x+c3sin2x © y= cze*+cze²¾…

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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: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

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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: Find the general solution of the given DE. y"-2y"-y'+ 2y 0 %D

A: NOTE: Refresh your page if you can't see any equations. . the auxiliary equation is given by

Q: Find the solution. y' = 5y + e-2x y-2, y(0) = 2 -15x 13e A) y = + 3e 2r1/3 23 139e 15x – 3e -2x \1/3…

A: Given differential equation is in the form of Bernoulli's differential equation.

Q: c) Show that y(x) = 1+ax+bx², where a and b are non-zero, is a solution to Laguerre's equation, d²y…

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Q: Obtain the general solution of the following: A. (D2 − 1)y = ex + 1 B. (D2 + 1)y = sec3x

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Q: 9. Find the general Solution of the following DE. a. (D - 4D2+ 4D)y = 0. b. (9D + 6D² + D)y = 0. c.…

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Q: Find the general solution of xy + 6y = 6x, VD. 3x a) O y2 7 b) O y2 3x* +C 9x8 c) Oy = + C 49 d) Oy…

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Q: Q(5) Find the general solution of (r+2y- 4)dr - (2r +y- 5)dy = 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: dy Find the general solution of xy + y² dr x2

A: According to our guideline, we can solve only first question of multiple question.So, here we solve…

Q: 20. What is the solution of (2x - y)dx + (4x + y – 6) dy = 0? a. (x+y- 3)° = c(2x + y – 4)² b.…

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Q: What is the general solution of (x2- xy + y2)dx – xydy = 0? %3D A. (x- y)ey/x = c B. (x- y)e*/y = c…

A: To find the general solution of the below differential equation. x2−xy+y2dx−xydy=0

Q: Find the solution. xy'+ xy = 1 - y, y(1) = 0 y = x-2(1 + el+*) Bx = y-(1 + e'-") y = x-(1 - e'-) D…

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Q: This is the solution of y" + 4y' + 3y = 8 (t – 2) , y (0) = 0, y' (0) = 0 O y = [e-t-2) –e-8(t-2)] U…

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Q: Suppose that y (t) =4 t e + B is a solution to y"-3y'-4y =-5e-4, where {A, B, a} are constant…

A: The given differential equation is  y'''-3y'-4y=-5e-t-4 and the given solution is particular…

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

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Q: 17 c. Find the general solution of the D.E. 2 y" +4y'-8y = 8×-4e²* +4

A: We solve given DE by using method of undetermined coefficient.

Q: (D³+3D²– 4D)y = 0 -4x Question 5 Find the solution. dy 31+9y=2ty 5/3 dt

A: P

Q: Find the particular solution: t- 2y 2t3, y(-2) = 4 dy %3D OA y (2t+ 3)t2 OB. y (t+2)t² OC. y (t+3)t2…

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Q: Solve: (D² + 5DD' + 6D²)z = (y – 1)e* + sin(2x – 3y) + 3x + y, where D =- and ax D' = y = 2 ду

A: Given partial differential equation is, This is a homogeneous partial differential equation with…

Q: 'ind the general solution of d³y 6. dr3 dy - 8y = 21e2 dr dr2

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Q: Fınd the general solution of d²y dy + 2x - 2y = 0 dx dx² where y(x) = x is a solution.

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