Can someone please explain how associated homogeneous linear differential equations work with an example?
2026-03-26 04:28:51.1774499331
associated homogeneous linear differential equations
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Lets say you have the linear differential equation $y'' + y =3x$;
The associated homogeneous equation is $y'' + y = 0$
The set of the solutions to the homogeneous equation is {$\alpha \cos +\beta \sin ; \alpha, \beta \in \Bbb R$}.
One particular solution to the innitial equation is 3x.
Thus theset of solutions to the initial equation is {$\alpha \cos x +\beta \sin x + 3x; \alpha, \beta \in \Bbb R$}.