Differential Equations - 22 - Why superimpose? (y=c1y1+c2y2)

[@ryansih4886]

linearsecondorderconstantcoefficienthomogenousequation hahaha keep up the good work

[@uselessdiscussion7355]

This right here is crazy lol I think it's starting to make sense. Because it's linear, it's actually just like taking the differential equation evaluated at y1, and adding that to the differential equation evaluated at y2. Since each is a solution, each differential equation itself is 0 = 0, and so that equation plus itself is still 0 = 0 and is still totally a solution/valid. Wow!

[@TheLazyEngineer]

Useless Discussion exactly!

[@mohfa1806]

Thank you for your great videos I have question : if we look at it geometrically then Y1 and Y2 and Y=Y1+Y2 are three different functions that satifies our differential equation , so we will draw three different functions that are totally different when C1 and C2 are non zero . Accordingly how Y includes Y1 and Y2 knowing that graphically they are totally different functions ? Thank you

[@Ahmad-gn1pd]

To be able to put two intial conditions

[@senurahansaja3287]

What if one solution is zero, then do we need to write it as y= c1 + c2e

[@rfaatsoliby8796]

thank you man