Solution of Differential Equations Reducible to Linear Form

When the given diff. equation is of the type

dy/dx + Py = Qyⁿ and P and Q are constants or functions of x alone and value of x is not either zero or one, the equation can be reduced to the linear form.

Procedure:

Divide both sides by yⁿ

y^-ndy/dx + Py^-n+1 = Q

Substitute y^-n+1 = v

we get the transformed equation which is a linear equation

dv/dx + (1-n)Pv = (1-n)Q