In the process of finding the orthogonal trajectories, a student determined that the differential equation corresponding to the given family of curves has the following form: dy y? – x² 2xy %3D dx What is the differential equation of the orthogonal family? dy 2xy dx y? – x2 O 2xydy = (y? – x2)dx 2xy o dy v² – x? y² – x² dx O dy dx 2xy

Q: Consider the equation dy dx = y - 4x x-y which is not separable. (a). Show that the above equation…

A: Step 1: Step 2: Step 3: Step 4:

Q: dy B. Find the first derivative of the following: dx 1. x³+4xy − 3y4/3 = 2x - 2. y=√x.csc (23x)

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the differential of the function. H = x5y4 + y9z³ dH = Jdx + 1dy + 1) dz

A:

Q: If the length of a curve from (0,–3) to (3,3) is given by [ V1+(x² – 1)² dx , which of the following…

A: Length of a curve formula.

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.