Classify each of the following equations as to order and degree. dy + (ху — сos x)dx %3D 0 d²Q + R dt2 1) dQ. Q 2) +-= 0 dt 3) у" + ху" + 2у(у')? + ху %3D 0

Q: Find and at the given point without eliminating the parameter. x = Vi, y = 21 + 309; † = 1. dy

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Q: Which of the following equations determines E(XY)? xy(x, y)dxdy (x, y) / fv(x, y)dydx // xwfr (x,…

A: Solution

Q: What is the point of intersection of the given DE (x + 2y – 1)dx – (2x + y – 5)dy = 0 ? Select the…

A: Given,  DE : (x+2y-1)dx-(2x+y-5)dy=0

Q: If x"y" = (x+y)* m, m+n d'y prove that = 0 .2 dx?

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Q: dy 2х %3D (Зу + x)— dx

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Q: 16. If m/STU = (13x – 6)', mSƯ = (21x + 8)', and mUT = 143', find mST. %3D %3D U T

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Q: (у — ӕ + хусotx)dx + zdy — 0 y(0)= 3

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Q: d. Use your answers for parts a and b to estimate 1 -dx using the trapezoid rule with n=4

A: Approximate by trapezoid rule

Q: What is the numerical approximation to 1 3 -dx -1 2+x using the basic trapezoidal rule? (а) 0 (b) 2…

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Q: If W = 2x3 + 3y², a 5t2, y = 2t³ %3D = %3D dW then find at t= 1 dt O 1912 O None O 1273 O 1572 2212

A: A detailed solution is given below

Q: If yo is the particular solution of dy 4x y, y(0) = 3, dx find the value of yo(2).

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Q: Find (au/ay), at the point (u,v) =(√2,3), if x = u² + v² and y= uv. ди (2) = (Simplify your answer.)…

A: Given query is to find indicated partial derivative.

Q: Transform the equation dy = ry into a variable da separable form. O vydy = xdx dy dy Vydy de %3D

A: We will transform the given equation into variable separable form as shown below

Q: In the given Bernoulli's equation 6y²dx – x(2x³ + y)dy = 0, what is ƒ P,(y)dy?

A: I have appended the formula used in the solution part

Q: Ir 9- ((2, y) | 2553,1SyS 3): D then: dz dy = %3D

A: Given D={(x,y)|2<=x<=3,1<=y<=3}

Q: Given z = 11sint + 18 and y= 11 cost + 45 (*) da %3D dt (i) (**) dy (0) dz %3D

A: Given that, x and y are parametric functions

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: Given z = 15 In(t) and y = 225 t then find %3D dy dx d'y dr2

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Q: If yo is the particular solution of dy 4x°y, y(0) = 3, %3D %3D dx find the value of yo(2).

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Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: Given y - xy? – x²y=2. Then, at the point (1,2), -is dx Blank 1

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Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

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Q: dz dz and at the point (3, 6, 1) where z is defined implicitly by the equation z4 + z?x2 - y - 4 =…

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Q: Show that if y = cosx/x , then d^2y/dx^2 + 2dy/dx+ y = 0

A: y=cosxx Differentiating with respect to x, we get dydx=dcosxdx·x-dxdx·cosxx2…

Q: show that if y=cosx/x, then d^y/dx^2+2dy/xdx+y=0

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Q: a A = and if xy = 1, then det ( AAT ) is equal %3D to y a

A: Given:A=axyaif xy=1 then detAAT=?

Q: 5. dy 4y-3x 2x-y dx

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Q: 4)Solve the followingIVPusing LaplaceTransform y′′−10y′+9y=5t,y(0)=−1, y′(0)=2

A: The differential equation is given as y''-10y'+9y=5t Apply Laplace on both sides, we get…

Q: dy у %3D (1 -3х)сos(?), then dx

A: Given, y=1-3xcosx Let us apply exponent rule: ab=eblna y=1-3xcosx=ecosxln1-3xDifferentiate…

Q: 2 5. x = 1+t2 2 y= t(1+t?)

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Q: 9. Find y", given y = %3D Vx-1

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Q: хdу — dy %3D (3x? — 3х)dx — ydx

A: The solution is given as

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: Transform the equation 2 (y + 1) dr – ydy = 0 into the form of variable separable. O 2zdz y (y+1) dy…

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Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

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Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: What is the value of the arbitrary constant of the given DE (3x + 2y + 7)dx + (2x – y)dy = 0 at…

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: Find (au/ay) at the point (u,v)=(√6,-2), if x=u² + v² and y = uv. du = (Simplify your answer.) dy)…

A: ANSWER: 1

Q: ,u = TX, X - 1 %3D %3D (Cosuz 4 dy

A: Differentiation using chain rule

Q: Use the equation e = 2xyz+1 to find %3D az/əx and əz/ay.

A: We have to find

Q: dx dy If L = Va? + y?, = -5, and dt = 2, find dt dL when a = 3 and y = 7. dt %3D dL dt

A: Given query is the derivative of L over t at x = 3 and y = 7.

Q: differentiate. a) g(t)こ3-2t St +1 c) H(u)= (u-JJ) (utro) d) FLt)- モ-3 %3D

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Q: Solve the following problem %3D 0, 0 0, + dx² ' ay? u(0, у) —D 1, u(п, у) %—D 0, и(х, 0) %3D 0, и(х,…

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Q: dy Q(1) If dr 2.ry r, y(0) = 0, find y(1). %3D %3D

A: According to experts guidelines of bartleby i have to solve first question. So repost for further…

Q: Given z = 10 In(t) and y = 100 t² then find %3D dy da d'y da2

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