Hello all! i have a doubt,consider a 2nd order ODE ,F[y]=y''+y'+y=0,it is said to be homogenous because F[ay]=aF[y],(where a is some constant) take this eqn where F[y]=y''+y'+y=3 ,it is said to be non homogenous because F[y] can be expressed as y''+y'+y-3=0 and thus F[ay] is not equal to aF[y],but if i take F[y] as y''+y'+y which is equal to 3 i.e then F[ay]=ay''+ay'+ay=a[y''+y'+y]=a*3=aF[y],where did i make a mistake here?