Find the differential equation of the family of all straight lines passing through the origin - Business Mathematics and Statistics

Find the differential equation of the family of all straight lines passing through the origin

Sum

The general equation for a family of lines passing through the origin is

y = mx .........(1)

Differentiating w.r.t x,

`("d"y)/("d"x)` = m .......(2)

Using (2) in (1)

y = `(("d"y)/("d"x)) x` is the required differential equation

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Formation of Ordinary Differential Equations

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Chapter 4: Differential Equations - Exercise 4.1 [Page 85]

Chapter 4 Differential Equations
Exercise 4.1 | Q 4 | Page 85

Find the order and degree of the following differential equation:

`("d"^2y)/("d"x^2) = sqrt(y - ("d"y)/("d"x))`

Find the order and degree of the following differential equation:

`("d"^2y)/("d"x^2) + y + (("d"y)/("d"x) - ("d"^3y)/("d"x^3))^(3/2)` = 0

Find the differential equation of the following:

y = cx + c – c³

Find the differential equation of the following:

y = c(x – c)²

Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x-axis