For the differential equation y(n) + P₁(t)y(n-¹)+...+Pn(t)y=0 with solutions Yı, •, yn Abel's formula for Wronskian is yn) (t) = ce-Spi(t) dt " W (y₁, Use Abel's formula to find the Wronskian of a fundamental set of solutions of the differential equation ty(4) + 5ty""+y" - 4y = 0. NOTE: Use c for the constant of integration. W(y₁, y2, Y3) (t) =

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A: We need to find equation of polar curve.

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A: Topic = Application of Derivative

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A: We will solve.

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A: The DE is given as , y''+2y'+y=e-tlnt find the solution by variation of parameters.

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Q: Evaluate the iterated integral. 2 . (x+y+z) dx dz dy

A: The given integral is: I=∫02∫08∫01x+y+zdxdzdy   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

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Q: Sketch the solid whose volume is given by the iterated integral and rewrite the integral using the…

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Q: Evaluate the iterated integral. 2 √4-3²3-8²-12² SS S x dz dy dx 0 -S+x² + y²

A: Given, ∫02∫04-x2∫-5+x2+y23-x2-y2xdzdydx

Q: Decide which of the two given functions is linear and find its equation. 12 3 4 X 0 f(x) 9 14 g(x)…

A: Topic = Functions

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Q: We have verified that x and x are linearly independent solutions of the following second-order,…

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Q: Find the general solution of the given second-order differential equation. 20y" 11y' 3y = 0 y(x) =

A: The given differential equation is: 20y''-11y'-3y=0   So, we can also write as; 20D2-11D-3y=0 The…

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Q: Find ||FI|. F(x, y) = i + j Sketch several representative vectors in the vector field. y O O -4 -2…

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Q: Find the derivative of the function using Chain Rule. Given f(x)=(x²+x-3)√√x²+x-3

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Q: A vector with magnitude 9 points in a direction 160 degrees counterclockwise from the positive x…

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Q: Find the average value have of the function h on the given interval. h(u) = (In(u))/u, [1, 6] have =…

A: The function is given as , hu=lnuu find the average value have on 1,6.

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.

A: Topic = Functions

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A: Given function: g(x,y)=ye-x

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A: We have to estimate the given function.

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A: Find the general solution of the given higher-order differential equation.

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Q: What is ette-t At- ○ - In [e* O ○ ○ dx e* + C] In [e* + e* + C In [e* e*] + C -In [ee] + C

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Q: Find the curve of best fit of the type y = aebx to the following data by the method of least…

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Q: Evaluate the integral. if -2 ≤x≤0 [₁ f(x) dx where f(x)=4-x² if 0<x≤4 22 x Enhanced Feedback Please…

A: Here we have to find the integral.

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A: The given polynomial gx=-10x3-8x2+8x-4

Q: part, and you will not be able to come back to the skipped part. Tutorial Exercise Solve the…

A: The given differential equation is;  y''+3y'+2y=1/(8+ex).

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Given differential equation y""-ay" -4y' + 8y = e²-³x +8x⁹ (D³ - 20² - Auxilary equation 2 4D +8)y=e…

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A: We can evaluate the given iterated integral.

Q: 11

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