ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

Q: O Solve y' = x + y + xy, y(0) = 1 by choosing step length 0.2 for y(0.4) by Euler's modified ethod

A: Given y'=x+y+xy, y(0)=1 Take f(x,y)=x+y+xy, Using the euler formula, Since it is given that h=0.2.…

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: solve the following diffrential c) x²(y+1)dx+(x²-1)(y-1)dy=0

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

A: Solution is given below:

Q: y=A + Cx is the general solution of the exact DEQ: y - xy' = 82. Determine A.

A: A differential equation is an equation in x,y and derivatives of y. A first order differential…

Q: Find the general solution of the DE: y"+y' + 2y = 0

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Q: Find the particular solution of y2dx+x(x+y)dy=0, when x=1, y=1. Let x=vy.

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Q: 4. xydx + (y √ x² + y²-x²) dy=0

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Q: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: Let y(x) be the solution for the DE : y' = (x + y – 1)² If y(0) = 1, then find y()

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Q: Find the solution. y'• ty ty" © y- (1-c, y- - (1-co")

A: We have to solve y'+ty=ty3 This can be written as: y'+ty=ty3⇒1y3y'+tyy3=t⇒1y3y'+ty2=t⇒1y3dydt+ty2=t…

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: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1   Find the general solution.

A: The given differential equation is: y''-y=4cost So, we can also write as: D2-1y=4cost So, the…

Q: Find the particular solution of y' = xey-x? given y(0) = 0.

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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: Find the solution to ty' – y = r² e 0.09 ' satisfying y(1) = 0 and valid for all t> 0.

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Q: Let y(x) be the solution for the DE : y = (x + y + 2)2 If y(0) = -2, then find y() ○2-푸 O 8 - T O -…

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Q: 5. Show that 1 T = VI? + y? satisfies the equation Tz + Tyy = T3

A: Given T(x,y)=1x2+y2

Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: 2. Obtain the particular solution when x = 0 and y = 1 (2 xy + x + x*) dc + x²) dy = 0 - (1 + 4 |

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Q: Find the wrong Kian W(y1,y2)(t) of y1 and y2  Where y1=t and y2= e^t are solutions of…

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Q: (r²+y + y³) dx – x dy=0

A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

Q: Find a particular solution to y"+2y' + y =t

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Q: Þ(x) = x² is an explicit solution to dy 2y dx ylgn ihi

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Q: Obtain the general solution. 1. y' = xy?

A: We will find out the required general solution.

Q: Let y(x) be the solution for the DE: y = (x+y+ 2)2 If y(0) = -2, then find y() %3D

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Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

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Q: Ex: FIND A COMPLETE SOLUTION OF EQ. y" + 3y" + 3y' + y = 0

A: The given differential equation is y'''+3y''+3y'+y=0. Find the complete solution of the differential…

Q: Let y(x) be the solution for the DE : У 3 (х +у-1)2 If y(0) = 1, then find y() 8 - JT JT Зл 4 Зл -…

A: Here to solve the given differential equation first we change the variable y by a  transformation .…

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: For x=e2 y=In 2t. find y' when x=e. O 4e e 4e O e -|

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Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: Find the particular solution of y²dx + x(x+y) dy=0., when x=1, y=1. Let x=vy

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

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Q: Show that y = In (x) is a solution of xy" + y² = 0.

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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: 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: Give the general solution to -y + 2 ху a) Os = + Cx² b) Oy =x+Cx? c) Oy = 7x o or - d) Oyl x² + Cx-…

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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: (D^2+1)y=10e^2x ; when x=0. y=0, y'=0. Ans: y=2(e^2x-cosx-2sinx)

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Q: Solve the homogenous diff equation of; xdx . (y+1) dy y³ e-x = 0

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Q: 2. Find te gunural soiUtion of 2

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

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Q: dy ind the general solution of = y + 2x. dz O a. y = x(Inx + c) O b. y = -x(lnx + c) O c.y = x2(2lnx…

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Q: 7= - + Cle2x general solution to the DE y"=2y+x Find C1 with the given condition y (1) =1/4

A: Given DE is y''=2y+xand the general solution is yx=-x3-14+C1e2xand given condition is y1=14find C1

Q: dy Find the solution of = y (8 – ) satisfying the initial condition y(0) = 144.

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Q: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: The general solution of the DE y" + 4y' = 0 where y(0) =1 and y'(0) = 8 is O None of these OF y = 3…

A: OPTION (b) IS CORRECT. THE GENERAL SOLUTION IS  y= 3-2e-4x