# Linearity / multilinearity in LDE(linear differential equations)

1. Oct 20, 2013

### shivaniits

hello everyone
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)..?
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..!!

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Last edited: Oct 20, 2013