2. Let y = f(x) be a particular solution to dy x+y Consider the point (1, –1). Does f have a relative dx 1+y2* minimum, relative maximum, or neither at that point? Justify your answer.

Q: Find the goveming equation and associated boundary conditions by minimizing the functional, I.…

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Q: dy sin x - y where f(n) = 0. dx %D |

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Q: From (1) (Y + x*y +2x2) dx +(x + 4×y" + ® y³) dy = 0 - ydx + xydx + 2x²dx + xdy + 4xy"dy +oyy =(Y.dx…

A: We will find out the required solution.

Q: Find dy and Ay for y = 3/x –1+ 2x at x = 2 with dr = Ar = 0.2.

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Q: 1 Let y = -. Find dy and Ay at x = 7 with dx = Ax = – 1. Enter the exact answers. dy = Ay =

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Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

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Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: 19 271. dx y= 1-X) dy = -Ldx -dy= dx S-(-yei) y" dy 99 99 100 100 99 dy dy 100 %3D + R00 100 ). %3D…

A: Refer below

Q: If the equilibrium of dy/dx = y - sqrt(y) when y>0 is y=1, is it a stable or unstable equilibrium?

A: Given dydx=y−y, when y>0 We have to check whether y=1 is stable or unstable equilibrium. Note:-…

Q: 2. Identify the 3rd order nonlinear DE. 3 (dy` A. ( +x³y – xy³ = 0 dx. d³y d²y +y dx2 В. = 0 dx3 d³y…

A: Check each options while it is 3rd order as well as nonlinear differential equation.

Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: If y = x3 – 2x2 + 3 and x = t² + 2 find dy at t=2. dt %3D

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Q: 1 Let y = -. Find dy and Ay at x = 8 with dx = Ax = –1. х Enter the exact answers. dy = Ay =

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Q: Suppose lim y(t) = 5, which initial value problem does y satis dy A. = 25y – y", y(0) = 6. dy В. =…

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Q: · Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x 0 to…

A: The given differential equation is,  dydx=y'=-3y+2e-x with an initial condition y0=2.  For…

Q: 6. What can you conclude when dy is changing dx from positive to negative? A) fis at a local minimum…

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Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx - (x +…

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Q: If y = f(x) is the solution of (5aty – 12a – 2y³)dx + (x³ + 4y³ – 6xy?)dy = 0, f(0) = 0, then

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Q: Construct the Green's function for d²y dx² dy + (k?x² – 1)y = 0, + x dx subject to the boundary…

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: The solution of dy/dx = y2 with initial value y (0) = 1 bounded in the interval %3D

A: Introduction :

Q: True or False: For an IVP dy/dx = f(x,y); y(a)=b, if f(x,y) is not continuous near (a,b), then its…

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Q: Solve the D.E [y(++csy)]dx + [x+Inx-xSiny] dy-o

A: Solve de

Q: If y is a function of x, then the equation (y - a)dx + 3ry dy = 0 is not linear + but both + and…

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Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: Find the domain of the initial-value problem and determine its interval of existence (i.e domain of…

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Q: Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x = 0 to…

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Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: 1. Show that the solution of: dy x? y 1.1 with initial condition , y(1) = 2 dx 1+ x3 is y = V4 +…

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Q: OBTAIN A FAMILY OF SOLUTION 2. (x - yny + y In x ) dx + x CIn y - In x)dy =0 3. [x - yarctan…

A: This question is related to differential equation.

Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: 1.Find the critical points, classify each critical point as stable, unstable or semi-stable . dy 10…

A: Given: dydx=10+3y-y2 To Find: a. Critical Pointsb. Classify each critical point as stable, unstable…

Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx – (x +…

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Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: Let f(x,y)= 3+cos(x) sin(2y) a) Show that the function has a stationary point at (0,Pi/4). b) Is (0,…

A: To analyze the critical point (0,pi/4) of the given function of two variables

Q: For dy/dx = y2-3y classify the critical points as asympotically stable, unstable, or semi stable

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Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

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Q: Find the point at which the function f(r,y) = 2 in z+2 In y attains a maximum subject to the con-…

A: Maxima or minima: For any function f(x), 1) Evaluate f'(x)=0 for critical point. 2) Evaluate f''(x)…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: 1. Determine the general solution of (x 3y )dx – x dy = U

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Q: Hw #4 ( 2 xy +y -tany) dx+(x²-x tany tSeiy )dy =o ??

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

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Q: Find dr dy at x = -1 if y =u° +5u – 4 and u = x² +x.

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Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: Obtain a family of solution 1. [x-y arctan(y/x)]dx + x arctan (y/x)dy = 0

A: Solution is given below:

Q: Make the curve y = ax4 + bx³ + cx² + dx + e pass through the point (1, -8) be tangent to the line y=…

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