Someone explains to me what an associated homogeneous equation is and why with this we can obtain a solution for an equation, thank you and happy 2024!
#Associated homogeneous equation
wide bone
humble ravenBOT
spark ice
For a nonhomogeneous linear DE, you can find the associated homogeneous equation by putting the DE in standard form, then setting the RHS equal to 0. For example if you have a nonhomogeneous second order DE of the form $y'' + p(t)y' + q(t)y = G(t), G(t)\neq0$ you can get the associated homogeneous equation by doing $y'' + p(t)y' + q(t)y = 0$. usually this is useful for solving DEs with variation of parameters or method of undetermined coefficients
tall prairieBOT
animetrash
