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It is linear if when you write the equation in its implicit form the only mathematical operations that you have in the equation are addition, subtraction.

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Linear differential equations are those which can be reduced to the form L y = f, where L is some linear operator. Your first case is indeed linear, since it can be written as: (d 2 d x 2 − 2) y = ln ⁡ (x) While the second one is not. To see this first we regroup all .

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Jul 21,  · What is linear homogeneous equation? Definition A first order homogeneous linear differential equation is one of the form ˙y+p (t)y=0 or equivalently ˙y=−p (t)y. “Linear” in this definition indicates that both ˙y and y occur to the first power; “homogeneous” refers to the zero on the right hand side of the first form of the.