Find the orthogonal trajectories of family of curves x-y=cx^2

Q: race the following curve( x^2+y^2)x=2x^2+y^2   With all steps

A: The given curve is x2+y2x=2x2+y2. Trace the given curve with steps. x2+y2x=2x2+y2

Q: Evaluate the integral. [¹² (16+³ - 15+²+15+4) dt i

A: This is a question of vector Calculus.

Q: Use an appropriate local linear approximation to estimate the value (2.03)^3

A:

Q: orthogonal trajectories are curves in which their tangents at all points of intersection are at…

A: An Orthogonal Trajectory, of a family is defined as the group of curves that intersects each curve…

Q: given f(x,y)=ex^3 . y^8-x8y3 ,show that fxy=fyx

A:

Q: y = x – 2 + Ce* X-

A:

Q: Optimize the function f(x,y) = x^2+y^2 given the condition of x=y^2-5.

A: Answers are following in explanation step.Explanation:

Q: locate the critical points and determine the maxima and minima of a^3y=x^2(2a^2-x^2)

A: Given function is a3y=x2(2a2-x2)

Q: 1. y = - V2x +1 2. y = (x – 1)3 + 2 3. y =-1 2x 4. y? = 6– x 5. y = 1- |x|

A:

Q: Determine the relative extremes of F (X, Y) = 5X ^ 2 + 6Y ^ 2-XY if X + 2Y = 24

A: Given function is FX,Y=5X2+6Y2−XY and X+2Y=24. We have to find the relative extremes of the given…

Q: find the orthogonal trajectory of у^2-Сх^3-2

A:

Q: A parabola has the equation y^2 = -4ax. Determine the slope of the orthogonal trajectories. 2x/y O…

A:

Q: 13 4.

A: Slope of the curve at a point  is dy/dx at that point

Q: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

Q: Use the gradient descent method in the equation f=2(x_1)^2 + (x_2)^2 with the starting point (1,2)…

A: Given : equation                fx1, x2=2x12+x22 with starting point 1, 2 Use gradient descent in…

Q: Find the directions in which f increases and decreases most rapidly at point P. Then find the…

A: Step:-1

Q: IT Find the orthogonal trajectories to the given curve -3x y= 3x-1 + Ce C

A: With the help of derivative with respect to x and changes (dy)/(dx) by -(dx)/(dy) Then we find the…

Q: find the points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.