dy 4. Find the of the implicit function. dx 1 1 1 2 2 2 a

Q: dg 1 дд If g(x, y) = xy + y ln(ry), show that ду + y dr = x+ In(xy). dxðy

A: given: gx,y=xy+yln(xy) we have to show that: ∂g∂y-∂2g∂x∂y-y∂2g∂y2+1y∂g∂x=x+ln(xy)

Q: dy yf'(x)-y where f(x) is a given function. Solve dx %3D f(x)

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Q: Differentiate the given function. x-5 %3D x-2 dy %3D dx

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Q: dy = 1, find dt dx dL If L= x +y , -2, dt when x= 12 and y = 5. dt %3D dL (Simplify your answer.) dt

A: To find the derivative of the given function

Q: 1. (2y? + ye )dx + (4xy +xe + 2y)dy = 0 y(0) = 4

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Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5,…

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)

Q: H.w: find dy dx 1- y=-10x+3cosx

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Q: 3. (y-x)dx = xy (x dx + y dy)

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Q: dy = ay + by", dt a > 0, 6 > 0, -∞ < Yo < ∞

A: A differential equation is given by, dydt=ay+by2 for a&gt;0, b&gt;0, y0&gt;0. The objective is to…

Q: 1- find dy/dx as a function of x. y = 1³ – 4t

A: Note: According to bartleby we have to answer only question please upload the question separately.…

Q: E 34 ,8-23y² dz dx dy 3-3X p3-3X-y SSS(x+y+2)dy dx dz

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the solution of the following nonlinear ODE through separation of variables given that y(0)=1.…

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Q: 7. Given: y = 3 ; Find: dy/dt V16+tª -613 (16+t*) -2t3 (16+t*) (16+41) 글 (16+t*) ? (E) None of the…

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Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: H.W: Solve-Using D-operator dy dx dt ™ dt + 3y – 5x – e-t = 0 %3D dx dy 2 ++x + y – 3 = 0 dt dt

A: Answer is mentioned below

Q: Find the general solution of the given ODE. * (x + y – 1)dx – (x + y)dy= 0 -

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Q: dy = ky dx x = eky y = e-kx Option 2 O Option 4 O y = ekx x = e-ky Optio n 2

A: The given equation is dy/dx=ky.

Q: dy 5. dt = e&-t)secy(1+ t²). %3D

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Q: 2. Find by implicit differentiation. dy dx 4 (a) x +xy +y = 5 2 2 3 =D5 3 2. (b) x- xy + y 3. =D1

A: Recall: An equation of the form f(x ,y)=0 , in which y cannot be expressed directly in terms of…

Q: dy 10. Solve: dx x+3y (Hint: y = xv(x). ) х-у

A: The given data is: dydx=x+3yx-y         .....(1) To solve the given differential equation.

Q: dy Q.4 Find for the given function. dx y = In(x/2 /1 + x4)

A: I have stated the used formulas in the solution.

Q: dy implicitly: dx (12) Find (a) Iny = 2y2 – x (b) xey -y =x²-2

A: Given equation, ln (y) = 2y2 - x Differentiating both sides implicitly, =&gt; 1ydydx = 2(2y)dydx - 1…

Q: SOLVE BERNOULLI´S ODE y1/2 (dy/dx)+ y3/2 =1 ;   y(0)=4

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Q: dy Find if dx y = 7u + 2 and u = 9x-3. dy dx Enter your ar

A: Given:    f(x) = 7u + 2       u = 9x - 3

Q: xy + e^y = ln(x + y) defines y as a function of x implicitly for the most part. Express dy/dx in…

A: Given an equation, Where y is a function of x.

Q: 06: b: dw (1) Find if dt w= w = tanx and x = 4t³ + t.

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Q: 1² + 3x + 4 If t = (r² – 1) what is dt/dx?

A: We have to find derivative

Q: Q2: Find the for the following functions: dy dx 1. y = 1- and t = 1/ 2. y [In(x² + 2)²1³ 3. y = xsex

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Q: Find dy/dx of the given function. y = e 2x In x

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Q: dw if: dt Q1) Using the chain Rule to find w = xy + 3z, x = sint, y 2 cost, z=t (x2 +)

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Q: a) Find if y = (1+2/x)°.x²® using chain rule. dx dy 1-x b) Find if y = using chain rule. dx 1+x

A: (a) To find: dydx if y=1+2x3·x23 using chain rule: Formula used: Chain rule of derivative:…

Q: 2 -e dy=x(xdy-ydx).

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Q: (a) ſ sec(t) + tan(t) dt (b) ƒ&tlm»)* dx (1+ln(x))² 3x e2k (c) iesk dk 4+e4k

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Q: 5 To-4x D 5-2x NILS (6z²) dz dy dx

A: solution:-∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x6z3305-2x-y2dydx=∫0…

Q: dy for the following implicit function at p(1,1) Find dx Vxy +1 = y is O 1 O 1/2 O -1/2

A: A detailed solution is given below.

Q: Find the solution of the following ODE: dy y + 1+x2 0, y(0) = 1 1- %3D dx

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: Find dy at the given point. dx 17) 5xe9y= 12; (1,0) 18) x2 + 3y2 = 13; (1, 2)

A: Given that, 17)  5xe9y=12; 1,018) x2+3y2=13; 1,2 Find the derivative. Here we use the…

Q: Find d^2y/dx^2 for; x-t^2 y=Dt^5-2t^3+1 *

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Q: Q1. Solve the following linear ODES/IVPS. 1 dx а. 1 cost = cost, - х dt х dy t dt + 2y = 4e4t ;y(0)…

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Q: II. Find dy/dx of the following functions: 1. y = cosh √√4x²+3 2. y= sec hx² x² +1 3. y=xcsche4x

A: See this solution in below

Q: dy - f *P, = 7 dt y(0) = 4.

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Q: 4. ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e

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Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: d (F(x^) = ew dt %3D dx dx

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Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y (0) = 3

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Q: Use Green's function to solve: y"-4y' + 3y e, y(0) = 1, y'(0) 1.

A: Let y1x and y2x be the homogeneous solution of the initial value problem y''+pxy'+qxy=fx, yx0=y0 and…

Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y ( 0) = 3

A: We can solve the given differential equation by using initial condition.

Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

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Q: ) S3x'dx 34- 3/2 3) Ssú dy dt

A: