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Equation is linear if dependent variable is not in any other power than 1 e,g y

Equation is linear if dependent variable y is only being mulitiplied by constant.

Equation is linear if dependent variable y is not being multiplied by variable x

sin(y) and cos(y) make equation non linear.

Now i went to a site and they said following equation is linear

x^2y''+ xy' + (x^2-v^2)y = 0

y'' is being multiplied by x^2. and also y' being multiplied by x

Is there any easy way of steps to go thru to see if eq is linear or not besides the above mentioned...I am trying my best but i will be need lots of help with DE and I hope this forum will help me out.

Thnk you all