Solve by VP: y"' – 3y" + 2y' - et 1+e-x

Q: Solve y′′ + 4y = u2(t), y(0)=1, y’(0)=2

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Q: from y = ae + be %3D 2.

A: y=ae4x+be-4x ....(1) Differentiate both side w.r.t x dydx=4ae4x-be-4x        ....(2) From (1) and…

Q: Find curl (7z i + 8x j+4y k).

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Q: 3-Evaluate Fdr where 2X Cisgiven by rit) = t3+U-3t)rék

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Q: Solve the dff oq 2. 3. 3. %3D 1

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Q: Solve Ytt = = 4yxx 0 0 Yx(0, t) = 0, Yx(1, t) = 0, Y (x, 0) = 0, y(x, 0) = 3cos(2nx)

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Q: 'ind the Wronskian of any pair of solutions to 2t?y" + 3ty' – y = 0,t > 0.

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Q: 2. y" – y – 2y = 4e¬t %3D - -

A: Solve the differential equation

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: dy Use separation of variables to find the general solution to dr + 4xy? = 0. %3D

A: We have to sine given differential equation using seperation of variables

Q: dz where C is the bo + 6)

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Q: Verify that ry4 +r - 27 = 0 defines an implicit solution of the DE dy 4ry + 2y* + 3r = 0, dr on the…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

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: dz where C is ned by x = 0, :

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Q: Solve : dy- (- y) . Inn dy %3D ,13-1 Ordinery Dibberential equetion.

A: Solution:Givendydx=(1-y13)x2 ln xy13-1

Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

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Q: Verify by substitution that y(t) = Cekt - b/k is a solution ofy '(t) = ky + b, for real numbers b…

A: The given differential equation is y't=ky+b and the function is yt=Cekt-bk

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: Let x, y be the unique solution of x' = y y' = 0, y(0) = 1. = -x x (0) Show that x, y verify x2 + y?…

A: Given x' = y                   (1)y' = -x                (2)x(0) = 0                    (3)y(0) = 1…

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: dy 15 +4y-042

A: ∫115+4y-4y2dy

Q: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a have a…

A: Given: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a…

Q: S(2y + 3)?/ y+ 2 dy

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Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: -3y(In x)' +3x* (In x) y' =0

A: First simplyfy the given differential equation.Then taking integral on both sides and solve it.

Q: x, prove that y¨= 2(y² +1)(3y² +1).

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Q: у" — у' — х %3D 0

A: We are given: y'''-y'-x=0⇒y'''-y'=x Auxiliary equation is : m3-m=0⇒m(m2-1)=0⇒m=0, 1, -1 Hence,  CF=…

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: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

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Q: 6y" – 7y' – 5y = 2x³ + e¯* – 5 -

A: Ordinary differential equation involves the derivative of single dependent and single independent…

Q: Use the substitution u = (x – 1) to find S Tx-1) dr, |(x-1) giving your answer in terms of x.

A: Substitute as given in the question Take the derivative on both sides to write it in differential…

Q: dy of y3Dx dr Find csc2r,

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Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE

Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

A: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

Q: 11. Perpendicular to 5y = 2x – 6 and passes through the point (-1, 5)

A: Given, The line is perpendicular to 5y=2x-6 and It is passing through the point (-1, 5). Concept…

Q: 6) qyo -x² +2x + S%y +62=0 sty

A: 6)

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

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: What is the particular solution of 2xyy' = 1+y2 , when x =2, y = 3

A: The given differential equation is solved below in detail.

Q: Find mZR. Q 28 28-/2 R mZR = | %3D Submit

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Q: Use undetermined coefficients to find the particular solution to y'' + y' – 3y = 4t + 5 Yp(t) = %3D

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Q: Verify that y = c₁ex + c₂e4x is a solution to the DE: y" - 5y + 4y = 0.

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

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: Solve for y in terms of x and z. z = xy

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

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

A: Power series solution of the differential equation

Q: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: Eliminate the arbitrary conutantu 2. %3D y= ax + be

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