What is the order of the differential equation `dx/dy+ int y dx=x^3`?

Options

A. 1
B. 2
C. 3
D. cannot be determined

Answer

A

Explanation

` (dx)/(dy) + int y.dx =x^(3) Rightarrow int y. dx = x^(3) - (dx)/(dy)`
` Rightarrow 1+ (dy)/(dx) ( int y.dx) = x^(3) .(dy)/(dx)`
Differentiate both sides w.e.t.x
`Rightarrow0+(dy)/(dx) (y) +(inty.dx)((d^(2)y)/(dx^(2)))=x^(3)(d^(2)y)/(dx^(2)) + (dy)/(dx) (2x^(2))`
`Rightarrow y.(dy)/(dx)+(d^(2)y)/(dx^(2))[x^(3) -(dx)/(dy)]=x^(3).(d^(2)y)/(dx^(2))+2x^(2)(dy)/(dx)`
`Rightarrow y(dy)/(dx)+x^(3) (d^2y)/(dx^(2)) -((dx)/(dy))((d^(2)y)/(dx^(2)))=x^(3)(d^(2)y)/(dx^(2))+2x^(2)(dy)/(dx)`
` Rightarrow y(dy)/(dx) -(dx)/(dy) .(d^(2)y)/(dx^(2))=2x^(2) .(dy)/(dx)`
Multiplying both side by `(dy)/(dx)`