## How do you find the differential equation of the family of curves?

Table of Contents

The differential equation of the family of curves, x2=4b(y+b),b∈R, is:

- A. x2=2yy′−x.
- B. xy′′=y′
- C. x(y′)2=x−2yy′
- D. x(y′)2=x+2yy′

**What is the equation of family of curves?**

From the differential equation of the family of curves represented by y=acos(bx+c) where a, b, c are the arbitrary constants. Form the differential equation of the family of curves represented by y=acos(bx+c) where a, b, c are the arbitrary constants.

**What is a family of differential equation?**

The general solution of a differential equation contains a constant and therefore defines a family of functions all of whom satisfy the differential equation; they have similar, but slightly different graphs.

### What is the differential equation for the curve?

Geometrically, the differential equation y′ = 2 x says that at each point ( x, y) on some curve y = y( x), the slope is equal to 2 x. The solution obtained for the differential equation shows that this property is satisfied by any member of the family of curves y = x 2 + c (any only by such curves); see Figure 1 .

**What is the differential equation of the family of lines passing through the origin?**

xdy−ydx=0→ this is the differential equation of all straight lines passing through origin.

**What is the differential equation of the family of parabolas with vertex and focus on the Y axis?**

xdxdy=2y, which is the required differential equation.

## What is meant by family of curves?

A family of curves is a set of curves, each of which is given by a function or parametrization in which one or more of the parameters is variable. In general, the parameter(s) influence the shape of the curve in a way that is more complicated than a simple linear transformation.

**How are differential equations used in real life?**

Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. Also, in medical terms, they are used to check the growth of diseases in graphical representation.

**What is the differential equation that describes the family of lines passing through the origin?**

Differential Equations Consider the equation, y = mx, where m is the parameter. Thus, the above equation represents the family of lines which pass through the origin.

### What is the differential equation of the family of straight lines y equals MX?

y dx – x dy = 0. y dx + x dy = 0.