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.