Find the differential equation of the following y = cx + c – c3 - Business Mathematics and Statistics

Find the differential equation of the following:

y = cx + c – c³

Sum

y = cx + c – c³ ......(1)

Here c is a constant which has to be eliminated

Differentiating w.r.t x, `("d"y)/("d"x)` = c .......(2)

Using (2) in (1) we get,

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

Which 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 2. (i) | Page 85

Find the order and degree of the following differential equation:

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

Find the order and degree of the following differential equation:

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

Find the differential equation of the following:

y = c(x – c)²

Find the differential equation of the following:

xy = c²

Find the differential equation of the following:

x² + y² = a²