Consider the differential equation y" = ef + xy' where y is considered to be a function of . In this exercise, you will determine whether or not y = e + c is a solution to the differential equation for any constant c. (a) First substitute the above expression for y into the left side of the differential equation. In other words, compute y''. (b) Next substitute the above expression for y into the right side of the differential equation. In other words, compute e + xy'. (c) Based on your answers to (a) and (b), can we say that y = eT is a solution to the differential equation? O No O Yes

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A: We have to find PB→ and prove that M,N and C lie on the same line.

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A: Given∫ xsinxdx

Q: 2. Evaluate r sin rdr using integration by parts.

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A: Ans - In this question, we will find the limit of the given expression.

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A: To find dydx for the given y.

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A: Find potential function

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A: Follow the procedure given below.

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A: Topic:- algebra

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A: The given problem is solved below in detail.

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A: I am attaching image so that you understand each and every step.

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A: Let the vector v have an initial point at 2, -8 and a terminal point at -1, -8.To determine the…

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A: Given: y=√(x-2) , x-3y-2=0

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A: Given: I=∫xsinxdx   We know the basic integration formula. ∫sinxdx=-cosx+C∫cosxdx=sinx+C

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A: Given: x+5216+y-424=1

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A: Follow the procedure given below.

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A: topic- vectors

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A: Explanation of the answer is as follows

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A: The given function is: y=15x3+360x2

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A: I am attaching image so that you understand each and every step.

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A: We have to solve the problem using Euler's method.

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A: According to Bartleby guidelines I can only answer the first question of the given three questions.

Q: Show that the interval of convergence of the Series 2n-1 27-1 (4-3) IS given by -544/2 SWE

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A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

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A: Solved below

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A: We can solve this as follows:

Q: A) 0 B) 3 (C) 2 (D) 4 E 5 F) 1 Use polynomial long division to write 2x² + x³ 3x² + 4x-9 x² + x =…

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A: We have to find  directional derivative

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A: Explained below

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A: We have to evaluate the integrals.

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