Show that the function f(x, y) = (y + ax)?e+ax satisfies the equation given by ах dy?

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: dx xt x(1) = 2, solve for x(2) when h = 0.1 %| dt t²+2

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: Assume that x and y are both differentiable functions of t and are related by the equation…

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Q: CoS z 5,⁰ √1+4t2 dt, find F'(x) 11. If F(x) =

A: The objective is to find F'(x).

Q: A) The position of a particle P(x,y) at time t is given by: x= (2t +3) , y =+t.Find the distance it…

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Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Given that the first derivative of x^81+y^81=-36 is given by dy/dx=kx^c/y^c,what is the value of k?

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Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: x°y" + 2x?y"+ xy'-y=0

A: A homogenous linear differential equation with variable coefficients given by,…

Q: Express in form y=f(x) by eleminating the parameter x = t , y = tan−1(t3 + et )

A: It is given that,

Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

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Q: xdy – ydx – Vx²-y²dx = 0 хау — %3D

A: We have the equation xdy-ydx-x2-y2dx=0 This can be written as  xdy=ydx+x2-y2dx⇒dydx=y+x2-y2x We need…

Q: tan x d. y = sec? t dt 3 е. y = dx 1— х2. its

A: We have to find dy/dx for the given function

Q: Use Euler's method to estimate y(0.02) ey-x y' 1 + e²y ,y(0) = 4

A: Given differential equation is y'=ey-x1+e2y with the initial condition  y0=4 and step size is…

Q: Assuming 8x - y +7xy = 0 defines y as a differentiable function of x, use the theorem dx Fx to find…

A: By using partial differentiation .

Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: Show that f(x, y) = ln(x2 + y2) solves Laplace's equation, ∂2z ∂x2  +  ∂2z ∂y2  =…

A: Given Laplace’s equation is

Q: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

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

Q: Use Picard's method of successive approximation to solve the equation de 1+ xy, y(0) 1 at 8.1 X-0.1.

A: Given differential equation is  dydx=1+xy, y(0) = 1 To approximate the solution at x = 0.1 using…

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: |dx + N(x,y)dy = 0 x² + y,

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Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(xe^y) .

A: Solution:

Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: 2. In each exercise, obtain the particular of solution. a. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y…

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Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Use Euler's method to estimate y(0.02) ey-x y' = 1+e3y „y(0) = 4 0.01) What is the error in the…

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Q: Express in form y=f(x) by eleminating the parameter x = ln t , y = 2 − t

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Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

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Q: The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given by…

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Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x3+y4=3

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Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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Q: Find the directiona derivative of f (x, y) = In(e* – 4y at the point (0, 0) %3D - in the direction…

A: We have to solve

Q: Solve the differential eavations ydx xdy = 0 x' +y° +y?

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Q: Use the method of Green's function to solve y" + y = sint, y(0) = 1, y'(0) = -1.

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Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t