Question

Show that the function y = ax + 2a² is a solution of the differential equation `2(dy/dx)^2 + x(dy/dx) - y = 0`.

Answer 1

y = ax + 2a² 

Differentiate w.r.t. x

`dy/dx = a(1) = 0`

`dy/dx = a`

`2(dy/dx)^2 + x(dy/dx) - y = 2(a)^2 + x(a) - y`

= 2a² + ax – (ax + 2a²) [y = ax + 2a²]

= 2a² + ax – ax – 2a²

= 0

`2(dy/dx)^2 + x(dy/dx) - y = 0`

Hence, y = ax + 2a² is a solution of the differential equation `2(dy/dx)^2 + x(dy/dx) - y = 0`.