(2) Use variation of parameters to find a general solution of the following problem x(x² − 2)y" + (x² − 6)y″ + x(2 − x²)y' + (6 − x²)y = 2(x² − 2)² - given the homogeneous problem has FSS {e², e-, 1/x}

Q: (2x+1) (x+1) y"+2xy' - 2y = (2x+1)- A solution of the homogereous Jorm is → y= (x+1)-1 Find the…

A: The differential equation is provided below, 2x+1x+1y''+2xy'-2y=2x+12 And one of its solution is…

Q: If y(x) is a solution of xy" +(1-x)y' +6y = 0, find the value of y'(2). %3D

A: Given differential equation is xy'' +1-xy'+6y=0 -----(1) Also,  y'' +1-xxy'+6xy=0 Here,  limx→0…

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

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Q: 5. Find a second solution to (1 – a2) y" + 2xy' = 0, given one solution y1(x) = 1.

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Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: Find the general solution of 6y''+y"- 15y'=0, 3x 5x A y=c,x+cze 2 +Cze 3x 5x B y=c,+c,e ? +c.« ¯ 2…

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Q: 1) Find the Solution. a) (y" - 5 y² + 4y = 0 y(0)=4 5) 4'(0) = 0 " 4" "y" + "y' 4(1) = 5 y' (1)=10 +…

A: We have to find the solution of the given differential equation.Note: According to the guidelines we…

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

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Q: (b) Determine the general solution for y" - 2y + 5y = 0 and the solution of the IVP y" - 2y + 5y =…

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Q: Find the particular solution of y' =(2x)/1+2y y(2)=0

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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: P(x)y" + Q(x)y' + R(x)y = 0 is said to be exact if it can be written in the form (P(x)y')' +…

A: Step 1: Step 2: Step 3: Step 4:

Q: 2c) find the general solution to 9y"(x) +12y'(x) + 32y(x) = x +e*

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Q: The general solution of x' = 2x + 5y and y' = -2x - 4y

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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: 2. Solve IVP y" – 4y' + 4y = 0; y(1) = 1, y'(1) = 1 Cind a general solution

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Q: (10) Find the general solution of y" − x²y' + xy = x - if a solution of homogeneous part is y₁(x)

A: i have attached the solution image. please check it.Explanation:

Q: Find the solution of y"-y'-6y = -e* +12x with y(0)=1, y'(0)=-2 by method of undetermined…

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Q: Find the solution of y" – 2y' + y = 36 et with y(0) 6 and y' (0) = 5.

A: Given

Q: (3) Find a fundamental set of solutions to xy" - (2x + 2)y' + (x + 2)y = 0 given that Y₁e is a…

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Q: Solve the initial value problems: (a) / = 6+ 5y + y?; y(0) = 0 (b) / + 2.ry + ryt = 0; y(0) = 1

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Q: Show that the problem y" + (1 + X)y' + Xy = : 0, 0 < x < 1 y'(0) = y(1) = 0 has only the trivial…

A: To solve this problem, let's assume a solution of the form y(x)=emx, where  m  is a constant to be…

Q: 3) Assume that y, (a) is a solution to y" + P(x)y' +Q(x)y= 0. Prove that -SP(z)dz = - y} (x) y₂(x) =…

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Q: Determine the value of k such that y=4x²-3e²t is a solution to x(1-x)y"+ (2x²-1) y'+k(2x-1)y=0

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Q: 2) Find a general solution for y" + 8y + 16y 0 then find the particular solution for which y(0) = 1…

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Q: Verify (do not solve) that y(x) = 3x + 2x-1/3 is a solution to 3xy' + y = 12x.

A: Solution is    y(x) = 3x + 2x-1/3 Now to verify differentiate the solution w.r.to x .

Q: Find the general solution of the following DE. y' = 3 (y + 1) O y = 3ce³x - 1 Oy = ce³x - 1 Oy =…

A: y' = 3(y+1) dy/dx = 3(y+1) dy/3(y+1) = dx dy/(y+1) = 3dx now apply both side integration

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

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Q: Determine the value of k such that y = 4x²_3e²r is a solution to x(1-x)y"+ (2x² − 1) y' + k (2x −…

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Q: It is known that the two basic solutions of y" +b (x equation y" + b (x) y' +c(x) y = f (x) we use w…

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Q: (b) _x²y″ − 2xy' + (x²+2)y = 0, given solution y₁ = x sin x -

A: (b) The differential equation is given as , x2y''-2xy'+x2+2y=0              .....1