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

Q: xarctanydx + dy = 0 2(1+ y²)

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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: Obtain the particular solutions of the following: (y-Vr² + y² \dx– xdy =0, y(0)=1 a.

A: Solution is given below:

Q: Solve : t -4t y"+2y - Sydt e s(t-3) yco) = 0 y'co) = 0 %3D

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Q: Find the particular solution of xy" + xy' 13; y = 0 and y' = 1/2, when x = 1.

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Q: In the given question , find d2y /dx2 implicitly in terms of x and y :-   xy - 1 = 2x + y2

A: In the given question , find d2y /dx2 implicitly in terms of x and y :- xy - 1 = 2x + y2

Q: The solution to the initial value problem y" + 4y' +5y = 35e*, y'(0) = 1 is y(x) = ? -4x %3D %3D

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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: d²y - y = у 3 10sin?x %3| dx2

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Q: dy - y = e2*y³ dx

A: Let's Solve,

Q: 2. Find the general solution of the first-order equation dy _ y² – 2ry dr

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Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

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: Given the initial condition y(0) = 1, find the particular solution of the equation y' = e3x - 2y

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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: Find the general solution of the D.E (D^2+4)y=sin3x

A: We have to solve the problem

Q: Given the initial condition y(0) = 2, what i the particular solution of the equation √x - √ (x² +…

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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: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: Find the general solution to y" – xy' = 0. -

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Q: Solve for the solution of this D.E. y''' + 2y'' - 5y'-6y=0 Which has values of y=3, y'=6. y''=12…

A: Now , we have a homogenous differential equation . y'''+2y''-5y'-6y=0y(0)=3y'(0)=6y''(0)=12 We find…

Q: Obtain the general solution of the following equations:   (x-4y-9)dx-(4x+y-2)dy=0

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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: x² + y)dx + xy dy = 0

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Q: Q2: find the general solution: (D* - DD')z = (x² – 2y)e" + sin (2x – y) •2

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Q: Use the method of undetermined coefficients to solve the following initial value problem y" - 2y" +…

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

Q: nd the general solution to: 2yy -e^ = 0, |

A: The question is taken from the calculus in which we have to find  the general solution of  given…

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

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Q: Q5. Use the method of undetermined coefficients to solve (a) y" +2y' + y = x²e¬ª. (b) у" — 2у/ + 5у…

A: We are entitled to solve only one question at a time. As the specified one is not mentioned, So we…

Q: Q-1:B: Solve the initial value problem d?y + 4y = 8x2 ,y(0) = -3,y'(0) = 0 %3D %3D dx2

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Q: Obtain the general solution of the following equations:   1.) y(y3-x)dx+x(y3+x)dy=0

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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: a) Using the substitution z = y- 2r +3, solve the following initial value problem dy = 2+ Vy - 2x…

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Q: -4x e Find a particular solution to y" + 8y' + 16y= x3

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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: Find the particular solutions of the following equations: dy 4r +y given y-4, when x=1

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Q: Question included in image

A: Given that,

Q: Find the complete solution of ydx + (x + y²)dy = 0

A: Let us consider the differentiable equation of the form Mdx+Ndy=0 If ∂M∂y=∂N∂x then the solution is…

Q: Find the General Solution dy dr = y? – 3y²cos (x) 1.

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

Q: 3. xdy - [5x*(x²+y²) +y]dx= /x²+y² (xdx + ydy)

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Q: Solve the follawing D ·E. 2. y²dx + (3xy +y²-1) dy =0

A: Please refer the attached image for complete solution.

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: 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: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

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Q: 1. Find the solution of the DE: (D² + 2D + 5)y = 4e3t, y(0) = y'(0) = 0 using method of undetermined…

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Q: 3. Find the general solution of dy = y(xy – 1). d:r

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

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Q: 1: Find the general solution of the following equations: I. dy_2r+2y-3 X-y-1

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