1. Verify the two given function forms as a fundamental set of solutions of the DE on (-0,0) Check two things: are the solutions and are they linearly independent. 2. Form the general solution. DE: 4y" - 4y' +y = 0; ex2, xex2

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Q: Please solve

A: Consider the function

Q: A line 4x + y = 1 through the point A(2, −7) meets the line BC whose equation is 3x - 4y + 1 = 0 at…

A: Let the equation of BC be 3x-4y+1=0      ....(1) and the equation of AB be 4x+y-1=0         ....(2)…

Q: Solve for (x, y, z): 2x-2y+z=10 x+y-4z = - 17 3x-y + 2z = 13 O (4, -2, 1) O (1, -2, 4) O (2, 4, -1)

A: We have,  2x-2y+z=10 , x + y - 4z = -17 , 3x - y +2z = 13

Q: Find the general solution of x²y" + 10xy + 8y = x² Use the variation of parameters.

A:

Q: solve  w''' - 4w'' - 25w' + 100w = 0 how many linear independent solution to the equation needed…

A: solve  w''' - 4w'' - 25w' + 100w = 0 how many linear independent solution to the equation needed to…

Q: (a) Form the difference equation whose solution is yk = c1 + (c2+ csk)(-1)*, where c1, cz and cs are…

A: Given that the solution is yk=c1+c2+c3k-1k. To find the difference equation of this solution: For,…

Q: Find the equation of the tangent line at x = 2 for f(x) = 4+x-2x²-3x³. Write the answer in the form…

A:

Q: Find the equation(s) of the tangent line(s) to the graph of the curve y-x-12x through the point (1,…

A:

Q: B. Solve: If f(x)= x2 + 2, if x 0, find: 1. f(-4) 2. f(3).

A:

Q: is a solution of y"+ry 0 and write the

A: a) Unifom convergence of power series solution to the differential equation   implies that we can…

Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Given  f(x,y)=8x-2y+5 Find:f(2,-1) Substituting x=2 and y=-1 in the given equation, we get  f(2,…

Q: Show that the general cubic equation y3 + by2 + cy + d = 0can be transformed into an equation of the…

A: To find the equation of the form

Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

A: Let's find value of given function.

Q: Consider the equation x² + y³ + zª − 8xyz = z². Find z point (1,1,1). at the

A:

Q: Find the equation of the tangent line to (1,2) through the point . x + y + 3xy = 15 that goes Put…

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Q: The change of the energy efficiency function ( P ) of a factory with respect to uj and u2

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Q: 3.) The total weekly revenue( in dollars) that Depot realizes in producing and selling its speaker…

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Q: Which of the following is the special solution of the equation y" - y = 3x + 2 using the operator…

A: The given equation is; y''-y=3x+2