12-02-2014, 11:30 PM
Similar rules apply to multiple variable problems.
x' + y' = 0 is linear
x y' = 1 is non-linear because y' is not multiplied by a constant
Note, however, that an exception is made for the time variable t (ie. the variable that we are differentiating by). We can have any function of t appear in the equation, but still have an equation that is linear in x.
x'' + 2 x' + x = sin(t) is linear in x
x' + t2x = 0 is linear in x
x' + y' = 0 is linear
x y' = 1 is non-linear because y' is not multiplied by a constant
Note, however, that an exception is made for the time variable t (ie. the variable that we are differentiating by). We can have any function of t appear in the equation, but still have an equation that is linear in x.
x'' + 2 x' + x = sin(t) is linear in x
x' + t2x = 0 is linear in x