d²y 54. Let y = 4r+2r+l_find CL)

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: w = 4x + y² +2²³₁ x = ers²₁, y = 1 y = In(r+s).

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Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

Q: d (7) Vtan²s+ 21 dt = dx

A: Explanation of the answer is as follows

Q: Q. / Standx dx 3 None 2log|sec4x| + c 3 8log|sec4x| .+ c 3 2log|sec4x| + c 4

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Q: State fuo oer femnme egual JF.T ds gimn fow line into f.T ds givern that

A: In this question we have to find two other form of line integral.

Q: Evaluate the integrals

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: Evaluate fl. 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

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Q: dy Suppose that 2r² – xy + y² = 1. Find dr

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Q: dy If y = e8z+13 then- dx O 7e8z+13 O 13e8z+13 O 9e8z+13 O 8e8z+13 O 104e8z+13

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Q: 2. / Vy² – 4y + 10 dy

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+C₁e-ax using 2…

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Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: f(x, y) = In(4x + 3y) Calcule

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Q: f(x, y) = In(4x² - y) %3D

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Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

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Q: 2y*+1 dy 3

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Q: y" + 4y'+ 20y = 23sin t – 15cost y(0) = 0 , y'(0) = -1

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Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using 2…

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Q: 3 Evaluate 2z (4 – a – y) dy dæ.

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Q: b) y = In(xeVx + 2)

A: The solution are next step..

Q: Find dy if y= (4x+3)/(x2+6)

A: Quotient rule for derivative: ddxuv=vdu-udvv2

Q: aluate 2zy when Z =- and y = 3. %3D

A: From the given data

Q: 7 dy if Xy+2x +3y =1

A: We use implicit differentiate method to find dy/dx.

Q: dy If y = e7z+16 then- dx O 112e7z+16 O 8e7z+16 O 6e7z+16 O 7e7z+16 O 16e7z+16

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Q: dy dt = y(у — 4)(у — 8), до 20

A: see my solution

Q: 3 If y=/xL5x²_36 x²_3x²+Yx-12 (3 14 shuw that dy 24 dx4

A: firstly simplifying these expressions then , use the concept of differentiation

Q: 2₁ "+21y+8x=y" + 5y' + ex

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Q: Find dy/dr. y = esin 2x

A: We will use chain rule of differentiation to find the derivative.

Q: Show for Re(2) > 1 ez - 1dr = r'(z) 5(2). %3D 0,

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Q: 2. Find deri vative y T-2X y=3e6x %3D

A: Given,          y=3e6x+e1-2x

Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

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Q: can be obtained as dv dt -9. 81 – 0.0321 × v²

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Q: 2. dy 5y=Dy

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Q: dy 3y y torh(x) + 2

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Q: (b.) ry' + y = 1 In(r), with y(1) = 0

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Q: 2 lim y→7L_– 4y – 21 3y Зу — 17у — 28 -

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Q: T= tanh (x+ 2y+ 3Z) %3D finds O Tyy @ Tyx 3 Txy Tz Tzz Tzx @ Tzy

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Q: />(4y++ +9) * dy 12y2-

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Q: dy dt 13.1 y – 13.94 y²; y(0) = 0.03

A: Given,dydt=13.1y-13.94y2113.1y-13.94y2dy=dt1y13.1-13.94ydy=dtintegrating both the…

Q: 9. Find y if (a) y = 2" In (cot² (v7))

A: We are authorized to solve only one independent question, please repost remaining questions…

Q: (D + 3D + 2)y = xsin 2x

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Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: y” – 2y’ = ex (Non Homogenous DE)

A: Given DE is y” – 2y’ = ex.....(1) Let y=emx be trial solution of reduced equation of (1). Then…

Q: 33) - 2y + y, + y; = 0, y + y', = 4t +2, y, (0) = y, (0) = y,(0) = 0 y + y, = t² +2

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Q: Compute Δy/ Δx for the interval [2,4] where y = 5x−7.

A: ∆y∆x for function y=f(x) for the interval [a,b] = f(b)-f(a)b-a

Q: у" — 4y' + у %3D ex + 15

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Q: (4) y – 10y "+ 38y "– 64y '+40y = 153e¯* 111 %3D y "+10y "+ 34y '+ 40y = xe* +2e -4x + 2e cosx

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…