associated homogeneous linear differential equations











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Can someone please explain how associated homogeneous linear differential equations work with an example?






differential-equations differential homogeneous-equation







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    Can someone please explain how associated homogeneous linear differential equations work with an example?






    differential-equations differential homogeneous-equation







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      Can someone please explain how associated homogeneous linear differential equations work with an example?






      differential-equations differential homogeneous-equation







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      Can someone please explain how associated homogeneous linear differential equations work with an example?






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      differential-equations differential homogeneous-equation






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      asked Oct 16 '16 at 19:54









      Cory Browne

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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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.






          share|cite|improve this answer





















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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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.






            share|cite|improve this answer

























              up vote
              0
              down vote













              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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.






              share|cite|improve this answer























                up vote
                0
                down vote










                up vote
                0
                down vote









                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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.






                share|cite|improve this answer












                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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Oct 16 '16 at 19:59









                Astyx

                2,5901518




                2,5901518






























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