associated homogeneous linear differential equations
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Can someone please explain how associated homogeneous linear differential equations work with an example?
ordinary-differential-equations differential homogeneous-equation
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
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add a comment |
$begingroup$
Can someone please explain how associated homogeneous linear differential equations work with an example?
ordinary-differential-equations differential homogeneous-equation
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
$endgroup$
add a comment |
$begingroup$
Can someone please explain how associated homogeneous linear differential equations work with an example?
ordinary-differential-equations differential homogeneous-equation
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
$endgroup$
Can someone please explain how associated homogeneous linear differential equations work with an example?
ordinary-differential-equations differential homogeneous-equation
ordinary-differential-equations differential homogeneous-equation
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
asked Oct 16 '16 at 19:54
Cory BrowneCory Browne
2317
2317
add a comment |
add a comment |
1 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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
$endgroup$
add a comment |
$begingroup$
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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
$endgroup$
add a comment |
$begingroup$
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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
$endgroup$
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 {$alpha cos x +beta sin x + 3x; alpha, beta in Bbb R$}.
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
answered Oct 16 '16 at 19:59
AstyxAstyx
2,6091518
2,6091518
add a comment |
add a comment |
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