1. The problem statement, all variables and given/known data Is the following ODE linear? If so, is it homogeneous? xy'' + siny = 0, where y = y(x) 2. Relevant equations Linear = coefficients of unknown function y(x) and its derivatives only depend on x, not the unknown Homogeneous: can be written in form y'' + p(x)y' + q(x)y = 0 3. The attempt at a solution I'm confused in that the only way to get rid of the sin from the y is to put an arcsin in front of the y'' term. Can one just 'ignore' the sin and say it is linear and also homogeneous by the definitions above? Thanks for any help.