Are the functions y1 = xe*and y2 = e*linearly independent?

Q: equilibrium

A:

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

A:

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

A:

Q: (b) Find orthogonal trajectory of x2 - y = K. (Orthogonal trajectories]

A:

Q: Differentiate ysin(1/y)=1-xy

A:

Q: Find the linearization of y = at x = 16.

A:

Q: Which is the linear differantial equation into which the Bernolli differantial equation transforms

A:

Q: If X and Y have joint pdf given by

A: From the given information, fX,Yx,y=2I0,yxI0,1y                =2, 0<x<y, 0<y<1

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: 4) Find the orthogonal trajectories of the family of curves

A:

Q: y = x – 2 + Ce* X-

A:

Q: Compute the derivative: 3 | Vsin t dt dx

A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: Find both first partial derivatives, as well as fy for

A:

Q: Prove the relationship =<- dt

A: we have to calculate  ddt&lt;px&gt;  .....(1) &lt;px&gt;=-ih∫ψ*∂ψ∂xdx .....(2) substituting equation…

Q: Determine the orthogonal trajectories of the family of electric field lines described by the family…

A: Given    x-c3+y2-c23x-c=x3   differentiate  w.r.t.x    3x-c2+2ydydx-3c2=3x2⇒2ydydx=3x2-3x-c2+3c2…

Q: to***) dx . Refresh your integrating skills and evaluate

A: Answer

Q: Find the integrating factor of y'+ 3(x^2)y = 4(x^2)(y^2)

A: Divide the equation with y^2.

Q: Use a linear approximation (or differentials) to estimate the given number. 99.8 9.9

A:

Q: Find the orthogonal trajectories of the following family: y = Ce-x

A: First differentiate then  solve

Q: Use logarithmic differentiation to differentiate y = xV1+x². %3D Select one: dy xV1+x2 + 3 3(1+2r2)…

A: Given:

Q: Compute all second derivatives of f(1.y) = (x+) e- %3D

A:

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

A:

Q: What is the stability of equilibrium points of A and B? Is the energy of B higher than A?

A: If the vector field lines converge to the point or stay close to a point at all times the point of…

Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

A:

Q: Give the family of orthogonal trajectories for the equation: y2 = Cx5+5

A: To obtain the family of orthogonal trajectories for the equation: y2 = Cx5+5. Find a differential…

Q: Give the family of orthogonal trajectories of y^2=Cx^5+5.

A: To find →Family of orthogonal trajectories of y2=cx2+5 -1

Q: Find the orthogonal trajectories of y² = cx³

A:

Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: Does the differential dy represent the change in f or the change inthe linear approximation to f ?…

A: Given the differential is dy.

Q: Compute the partial derivative In(x² + xy).

A: ∂ ∂ xlnx2+xyTreat y as a constantApply chain Rule,∂ ∂ xlnx2+xy=1x2+xy∂ ∂ xx2+xy                    (…

Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: Use a linear approximation (or differentials) to  estimate the given number.  (1.999)4

A: Consider  1.9994

Q: Find the orthogonal trajectories of У — сх CX

A:

Q: Find both first partial derivatives. z = ln√xy

A: Given  z = ln√xy. We need to find both the first partial derivatives of the above function.

Q: Find the orthogonal trajectories of x^2+y^2−2cy=0

A:

Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

A:

Q: x2 - y2 + 2Cx = 0

A:

Q: 8. Find the orthogonal trajectories of CX

A:

Q: What is the integrating factor of y' - 2xy x?

A:

Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

A: To differentiate the given function

Q: 8. Find the orthogonal trajectories of y cx

A: