AP EAMCET Engineering 22 Apr 2019 Shift 1 Paper

Consider the equation,
y=(α+β+γ)x
Differentiate w.r.t x

dy

dx

=(α+β+γ)
= k
The order of above differential equation is 1 so. Statement I is false.
Consider the equation,
y=αx+β‌sin‌x+γex
Differentiate both sides w.r.t x .

dy

dx

=α+β‌cos‌x+γex ......(I)

d2y

dx2

=−β‌sin‌x+γex ....(II)
And,

d3y

dx3

=−β‌cos‌x+γex ....(III)
From equation (I) and (II), we get

d3y

dx3

−

d2y

dx2

=−β‌cos‌x+γex+β‌sin‌x−γex
=β‌sin‌x−β‌cos‌x
=β(sin‌x−cos‌x)
The order of above differential equation is 3 so. Statement II is true.