C. Eliminate the arbitrary constants in each equation and express the final answers in the following form: a,n(x)y(n) + an-1(x)yn-1) + . .. + a1(x)y' + ao(x)y – g(x) = 0 . 1. r* – y² = cy 2. y = cje" + cze²" + c3e*r

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Q: 5. Eliminate the arbitrary constant on the given equation: -4xy? + x°y2

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Q: 5. Eliminate the arbitrary constant on the given equation: -4xy2 + xy. C

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Q: 4. Solve the given nonhomogeneous( or undetermined coefficient( O.D.E by variation of parameters (1)…

A: In the first step find the complementary solution of the given differential equation:

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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: Q5. A. Solve the Euler-Cauchy equation xy - 4xy + 6y = 0

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Q: 5. Given that a cubic equation x" + ax" + bx +c = 0 has zerOS a, B and y. Show that aßy = -c.

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Q: Solve the DE x²y"+xy'+ (x²-÷) y=x³/2, given that Yı=x-1/2sinx and y2=x-1/2cosx are two solutions of…

A: Given the given DE is x2y"+xy'+x2-14y=x32. y1=x-12sinxy2=x-12cosx

Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: 4(a) Verify that the equation y = In(*/y) is an implicit solution of the IVP, ydx = (xy + x)dy y(e)…

A: Use the following formula ∫1xdx=ln|x|+c

Q: 5. Eliminate the arbitrary constant on the given equation: -4xy + xy2 = C

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Q: Use undetermined coefficients to find the particular solution to y'' - y = 4e t Y(t) =

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Q: 11. Determine the general solution of y" + y = tanx using variation of parameters a. y = C₁xsinx +…

A: We have to use Variation of Parameters to solve the differential equation. y'' + y = tan  x

Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

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Q: y" – 2y' + y = –3 – x + x²,

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Q: 5. Given that a cubic equation x° + ax² + bx +c= 0 has zeros a, ß and y. Show that aßy = -c.

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Q: 3. Find all solutions of the DE y"-12 y'+36 y=16 te (where t is a real constant) 6 x

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Q: 4. Give the graphical significance of the constant k for the equations of the form y=(x-h)³ +k

A: Given curve is y=(x-h)3+k

Q: 1. Eliminate the arbitrary constants on the given equation: Y = Ae" + Bxe™

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Q: Verify that y = h(x) =- (C is an arbitrary constant, x # 0) is a solution of xy' = -y.

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Q: The indicated function y(x) is a solution of the associated homogeneou Yp(x) of the given…

A: We will solve the given differential equation.

Q: 24. Find the particular solution that satisfies the initial condition. y'+y = 6e*, Initial…

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Q: Solve the following difference equation with initial conditions: 12Yn + Yn+1 = Yn+2, Y₁ = −2, Y₂ =…

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 x2 а у 2e + 2 - ex2 b. y =+…

A: The given differential equation is:y'=x3-2xywhich can be written asdydx+2xy=x3which is a first order…

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

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Q: Show that the equation Əy 2 a3y + 2k possesses solutions of the form 00 -kt E C,e cos (C, x+ E,) cos…

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Q: 1. Eliminate the arbitrary constants in the equation given by: (x- a)(y – b) = 1 |

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Q: Q/ Solve the differential equeion tx²y)dy=2xydx

A: The Given differential equation is: (x2-y2)dy = 2xy dx Rearranging the differential equation:…

Q: 4. Solve the given nonhomogeneous( or undetermined coefficient( O.D.E by variation of parameters (2)…

A: We have the given question,  This is a Euler-Cauchy Differential Equation of the form ax2y''(x) +…

Q: Show that the equation Əy + 2k Əx? possesses solutions of the form 00 2 c, e-kt 1" =0 Σ cos (a, x +…

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Q: . Find a particular solution to the inhomogeneous equation y" – 9y/ + 8y = e* in the form y(r) = c-…

A: To find A particular solution to the inhomogeneous equation in the form y(x) =Ce^(2x)

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Q: Use variation of parameters to find yp of x²y" - 2xy' + 2 y = -12 x(1/2) given that yi = x and y2 x2…

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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…

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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: 5. Give the graphical significance of the constant a for the equations of the form y-a(x-h)²+k.

A: We have to discuss the graphical significance of given equation.

Q: 3. Suppose = f(). (a) Given y(xo)= Yo, when does this equation have a unique solution? (b) Make a…

A: suppose dydx=fymx (a) given yx0=y0, when does this equation have a unique solution? we have  y'=fymx…

Q: Show that the equation dy + 2k possesses solutions of the form 00 Σ C,e -kt cos (a, x + E) cos (w,t+…

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Q: Find a general solution to the Cauchy-Euler equation x°y'"' - 8x²y" + 9xy' – 9y = x², x> 0,

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Q: Show that the equation dy + 2k possesses solutions of the form 00 - kt E c,e cos (oa,x+ E,) cos (w,…

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Q: Eliminate the arbitrary constant from the given equation: y=c1e2x cos3x +c2e2Xsin3x A y"=10y'-13y=0…

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Q: 1) Consider the equation y'+2x y-y'=-2x, x>0. (a) Determine the values of the constants k and r such…

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Q: 1) Find the general solution to the equation y(t) to 2y" + y – y = 3e-t + 2e¬t/2 Using the method of…

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Q: 1. Eliminate the arbitrary constants on the given equation: y = Ae" + Bæe

A: