Question

Determine the order and degree of the following differential equations.

Solution	D.E.
ax2 + by2 = 5	`xy(d^2y)/dx^2+ x(dy/dx)^2 = y dy/dx`

Answer 1

ax ² + by ² = 5

Differentiating w.r.t. x, we get

`2ax +2by dy/dx = 0` ....(i)

Again, differentiating w.r.t. x, we get

`2a + 2b(dy/dx)^2 + 2by ((d^2y)/dx^2) = 0` ........(ii)

From (i), we get

`a = - (by)/x(dy/dx)`

Substituting the value of a in (ii), we get

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

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

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

∴`x y((d^2y)/dx^2) + x(dy/dx)^2 =y((dy)/dx) `

∴ Given function is a solution of the given differential equation.