Question

The differential equation of orthogonal trajectories of family of 2x ^ 2 + y ^ 2 = cx is​

Answer 1

Answer: The differential equation of orthogonal trajectories of family of 2x²+ y² = cx is​ 2x² + 2xy dy/dx - y² = 0

Step-by-step explanation:

2x² + y² = cx

Step 1 : Taking derivative with respect to x on both sides, we get

4x + 2y dy/dx = c

Step 2: Substituting value of c in the equation of curve

2x² + y² = ( 4x + 2y dy/dx ) x

2x² + y² = 4x² + 2xy dy/dx

2x² + 2xy dy/dx - y² = 0

# SPJ2

Answer 2

Concept

The differential equation is an equation that relates one or more unknown functions and their derivates.

Given

2x ^ 2 + y ^ 2 = cx

To find

Differential equation

Explanation

The differential equation of orthogonal trajectories of family of 2x ^ 2 + y ^ 2 = cx is​ as under:

differentiating the equation with respect to x

4x+2ydy/dx=c

2y dy/dx=c-4x

dy/dx=(c-4x)/2y

put the value of y in the equation

dy/dx=(c-4x)2$\sqrt{cx-2x^{2} }$

Hence the differential equation is dy/dx=(c-4x)2$\sqrt{cx-2x^{2} }$

#SPJ3