But my lecturer wants us to explain without calculations. Is it that I can see how to explain by looking at the calculations?Try doing it with calculations and see what you get.
Hint: y=ax, y'=a and y" = 0.
i did the calculations and got the particular solution to be -20. Is the degree of x in the particular solution be the same as the r(x)? If theres no x in the r(x) before preliminary division, the particular solution will not have any x too?You are not seeing it by inspection, correct? So try solving it by doing the computation and then see if you can then understand that you did not need to do the computation.
What types of results do you get when you subtract two terms that are multiples of x's (like 9x-2x)?
I followed the hints and calculated 0 = 10, which proves that the particular solution ax does not satisfy the given DE, so how can i explain based on this?Try doing it with calculations and see what you get.
Hint: y=ax, y'=a and y" = 0.
If the differential equation is equal to a constant, the particular solution must also be a constant while \(\displaystyle y_p= ax\) is not a constant.I followed the hints and calculated 0 = 10, which proves that the particular solution ax does not satisfy the given DE, so how can i explain based on this?
But y=ax does yield a constant in that differential equation.If the differential equation is equal to a constant, the particular solution must also be a constant while \(\displaystyle y_p= ax\) is not a constant.