Solve the equation Utt + uraxa = 0, -000 u(x, 0) = f(x), ut(x,0)=0 for -00

Q: For what value of x will the curve y = x3 – 3x2 + 4 be concave upward?

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Q: Find the general solution valid near x=0 (x2 + 4) y" + 2xy' -12y = 0

A: We have to solve given problem:

Q: Ⓒ Solve зик subject to + 2x x = 0 u(x,0) = in Rx [0,00) n(x)

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Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: find general solution. dr/dt= -2tr,         r(0)=ro

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Q: Find a general solution valid near the origin: (x²+4)y" + 2xy' - 12y = 0

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Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Determine the interval of validity for the solution of the following IVP without solving it. (t2…

A: Given: t2-9y'+2y=ln20-4t, y4=-3 To Determine: Determine the interval of validity for the solutions…

Q: Obtain the particular solution of (3x2 - 2y2)y' = 2xy; x =0, y=-1.

A: We have to solve

Q: use Separation of Variables to find the general solution. yy' = x

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Q: Use variation of parameters to find a particular solution of y"- 2y' + y = 14xie Yp(x) =

A: Auxiliary equation for the given equation:

Q: Solve the differential equaton 2x2dy=(x+y)2dx

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Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

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Q: Use variation of parameters to find a particular solution of 14aie" 3 y" – 2y' + y - Yp(x)

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Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

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Q: Solve by partial fraction х 2 — 8 J2(x-1) dx 3 х ?(х —

A: Given: ∫x2-8x2x-13

Q: The integrating factor of the non exact DE ydx-xdy=- is -1/x^2, show your solution

A: We have to find

Q: xy' – y = 2x lnx

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Q: y' +(E- 1)y ==

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Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

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Q: solve the equation using differential equation linear in x and y: (2x-3y-5)dx + (3x-y-2)dy = 0;…

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Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

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Q: The general solution of the DE y"-y" + y'- y=0 is

A: We need to factorize this equation to find the solution.

Q: 5. Use variation of parameters method to solve а. a. y" – 2y' + y = 1+x2

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Q: 4. Solve Ar, = 3n2 + 4n - 1 with the initial condition r = 3. %3D

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Q: 6- Show that y = xsinx is a solution to y +y 2cosx

A: The given differential equation is: y''+y=2 cos x

Q: Find the solution of y-x =0 using separable variable method. dx

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Q: 3. Find the general solution using the method of Variation of Parameters. y" + y = = sect

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Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

Q: Find the particular solution of xy' – 2y = -x ; when x y = 5 1,

A: Recall: Consider the first differential equation                           dydx +P(x) y =Q(x)…

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: 2. x (х — 2)у" + 2(х — 1)у' — 2у %3D 0 |

A: Power series solution of the differential equation

Q: Solve: sec x = V2 + 2πkk e Z U + 2π시k E Z 3. + 2πkke z 2Tk k EZ 4. 4 + 2rk|k € Z 3 + 2rk|k E Z 3. of…

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Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: Use variation of parameters to find the general solution of y′′−2y′+ 2y=(e^x)csc(x)

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Q: The general solution of the DE y" -y" + y'-y 0 is

A: we have to find out the general solution of the differencial equation y'''-y''+y'-1=0

Q: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: Obtain the general solution valid near the origin: x(х — 2)у" + 2 (х — 1)у' — 2у 3D0

A: The differential equation has singularity at the origin. So we find the solution by Frobienius…

Q: 6- Show that y = xsinx is a solution to y= + y = 2cosx

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Q: Use variation of parameters to find a particular solution of y'' - Y = 4e-x 1-e-2x Yp (x) =

A: Solution of the differential equation, By using the method of Variation of perameters

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

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Q: 2. Solve the IVP: *+ 2y = te-2", y(1) = 0 dt

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