Differential Operator General Solution ... DN AxN-1 + BxN-2 + ..+C (D - a)N AxN-leax + BxN-2eax +.. (D? + B2) A cos(Bx) + Bsin(ßx) Given the differential equation у" - у' — бу %3 7sin(9x) The combined set of Differential Operators for this differential equation is (D2 + 81) (D -3)(D + 2) Find the General Solution for the differential equation. A y (x) = Acos(81x) + Bsin(81x) + Ce-3x + De2* y(x) = Acos(9x) + Bsin(9x) + Ce-3x De 2x y (x) = A e-3* cos (9x) + Be2 sin(9x) D D y(x) = Acos(9x) + Bsin(9x) + Ce* + De -2x y (x) = Asin(9x) + Be Ce2x -3x E F y(x) = Asin(9x) + Be* + Ce-2x

Q: Solving by variation of parameters 4y" 4y'- 8y 8e-*, we find that: O u_1=(-2/9) e^(-3x)and u_2=-(2/3...

A: Auxiliary equation and variations parameters

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A: series

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A: According to question,given Integral,Let I = ∫ cos-1x dx

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A: Given: ∫a4ln(ex)dx=6    

Q: To evaluate f dx, the integrand can be transformed to 1-sin?x

A: Follow the procedure given below

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A: Our Aim is to evaluate the integral given below:-∫x3+27x+3dx -(i)

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A: 2. The given limit is limx→21x2-4.   It is evaluated as follows: If limx→a-fx≠limx→a+fx then the lim...

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A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose d...

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A: Given slope of curve dydx=2x+b+12x3

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Q: Use the Law of Exponents to rewrite and simplify the expression. (a) b°(2b)3 (b) (6y³y4 2y5

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Q: A. How do you define Differentiation? B. Explain the principle of derivative with a given function, ...

A: Differentiation 

Q: Write the range in interval notation. Represent the gap with a "U". Find lim (secx) Find lim (secx)

A: We will graph the function and find out the range. 

Q: Y= --+ C1e2* general solution to the DE y"=2y+x Find C1 with the given + Cle2x 3 condition y (1) =1/...

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Q: 1. Determine the important parts of the conic and sketch their graph. а. у? + 2х — 10у — 31

A: As per our guidelines we are supposed to answer only one question i.e. the question no 1)a). For the...

Q: Evaluate the given limits numerically (using table of values) and graphically 1. lim2 X-2 x-2 f(x)

A: x 1.9 1.99 1.99 1.999 2.001 2.01 2.11 f(x) 3.9 3.99 3.999 4.001 4.01 4.1 4.11     limx→2x2-4x-2...

Q: What is an antiderivative of ... x²+1 x + arctan x – 5 2x + 3 x + arccot x x + 2arctan x + 1 А) в B)...

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Q: In Problems 59-66, use the price-demand equation to find the values of p for which demand is elastic...

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Q: dx 3.

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Q: dy If dx and y = 14 when x = 1, find y(2). 3x-2 27

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Q: 1. find the area enclosed by the x-axis and the curve y= -x^2+9

A: The region enclosed by the x-axis and the curve y=-x2+9

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Q: *Problems Involving Continuity A. Tell whether each given function has a solution on the indicated c...

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Q: Examine the following functions for maxima-minima and trace the curves. a. Y = x* +1 a²x b. Y=- a²+x...

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Q: x* + x³ + x² – x + 1 x(x² + 1)²

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Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is x...

A: Given query is to rewrite the integrand in integrable manner.

Q: Find

A: Solution is here

Q: For the Ordinary DE y '= f (x, y) to be guaranteed to have a unique solution containing the point (x...

A: Here we have to find when the ordinary differential equation y'=f(x,y) to be guaranteed to have a un...

Q: 8. Sum of the products of a constant and a variable: Ecx, = cx, +cx2 +...+cx, i=1 = c(x1 +x2 +...+x,...

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Q: Given f (x) = {r²+ k_ if-1< x skx – 3 if x<-1 | . Find the value of k such that lim f(x) exists. X--...

A: Topic = Functions

Q: 1. (D2 + 2D + 4)y = 8x? + 12e-*

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Q: The given problem needs the first derivative. Find the first derivative. a² x Y= a² + x

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Q: The slope of curve is given as (2x + b+) and has a value of 17 at x = 2. What is the value 16 of y w...

A: Topic = Integration

Q: The Laplace Transform of

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Q: Given an ordinary differential equation in the form: (xy + y² + y)dx – (x + 2y)dy = 0 (Eq. Test the ...

A: According to question,Given Differential equation,xy + y2 + y dx - x + 2y dy = 0

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Q: 1. Find the indicated values. f(g(8)) |x| f(x) g(x) s(8(5)) 1 5 g(f(5)) 2 5 8(5(3)) 3 2 4 4 1 S(S(4)...

A: Use the given table for finding the value of function 

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Q: uity?

A: We will find the functional value at x=2.

Q: Given a function whose graph is shown below. 1 0.5 -5 -4 1 2 -0.5사 -1.5 Determine lim f(x). r--1

A: We have the find the limit of f(x) at x = -1 using the graph of f(x).