we demonstrate the linearity in a function by a superposition principle..as in f(x)=y
f(x1+x2)=f(x1)+f(x2)
but that' the case when we have a single variable as x and if we have two variables then we modify the concept of linearity to multilinearity where f(x,y)=z
can never be represented as: f(x1+x2,y1+y2)=f(x1,y1)+f(x2,y2)
but if we have to apply the concept of multilinearity in LDE(linear differential equations)..?

Question

we demonstrate the linearity in a function by a superposition principle..as in f(x)=y
f(x1+x2)=f(x1)+f(x2)
but that' the case when we have a single variable as x and if we have two variables then we modify the concept of linearity to multilinearity where f(x,y)=z
can never be represented as: f(x1+x2,y1+y2)=f(x1,y1)+f(x2,y2)
but if we have to apply the concept of multilinearity in  LDE(linear differential equations)..?

shivaniits · Answer

well you will say what an idiot..i mean we have rules  to check if differential equation is linear or not(well my book says that)
the rules are: the differential equations are those in which the dependent variable and its derivative occur only in first degree and are not multiplied together
i tried to match this check for linearity against the one which we have been taught while solving equations..the superposition principle..
let me explain about what i am trying to ask with this super slow  typing speed 
please let me what do you think and do correct me if i am wrong in considering all this..!!

shivaniits · Answer

any idea or comment would be appreciated..!!