write a differential equation $(fracdydt = ay+b)$ whose solutions have the required behavior as t goes to infinity.
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
Let all other solutions diverge from $y = frac34$. write a differential equation $(fracdydt = ay +b)$ whose solutions have the required behavior as t goes to infinity. Explain how you came up with the differential equation).
I think the answer is $y' = 4y - 3$ but I am not sure. Can someone help me produce the answer with complete working?
differential-equations
edited Sep 22 '16 at 12:42
arash javan
1306
asked Sep 22 '16 at 12:07
Anonymous
214
add a comment |Â
up vote
1
down vote
favorite
Let all other solutions diverge from $y = frac34$. write a differential equation $(fracdydt = ay +b)$ whose solutions have the required behavior as t goes to infinity. Explain how you came up with the differential equation).
I think the answer is $y' = 4y - 3$ but I am not sure. Can someone help me produce the answer with complete working?
differential-equations
edited Sep 22 '16 at 12:42
arash javan
1306
asked Sep 22 '16 at 12:07
Anonymous
214
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Let all other solutions diverge from $y = frac34$. write a differential equation $(fracdydt = ay +b)$ whose solutions have the required behavior as t goes to infinity. Explain how you came up with the differential equation).
I think the answer is $y' = 4y - 3$ but I am not sure. Can someone help me produce the answer with complete working?
differential-equations
edited Sep 22 '16 at 12:42
arash javan
1306
asked Sep 22 '16 at 12:07
Anonymous
214
Let all other solutions diverge from $y = frac34$. write a differential equation $(fracdydt = ay +b)$ whose solutions have the required behavior as t goes to infinity. Explain how you came up with the differential equation).
I think the answer is $y' = 4y - 3$ but I am not sure. Can someone help me produce the answer with complete working?
differential-equations
differential-equations
edited Sep 22 '16 at 12:42
arash javan
1306
asked Sep 22 '16 at 12:07
Anonymous
214
edited Sep 22 '16 at 12:42
arash javan
1306
asked Sep 22 '16 at 12:07
Anonymous
214
edited Sep 22 '16 at 12:42
arash javan
1306
edited Sep 22 '16 at 12:42
arash javan
1306
edited Sep 22 '16 at 12:42
arash javan
1306
1306
asked Sep 22 '16 at 12:07
Anonymous
214
asked Sep 22 '16 at 12:07
Anonymous
214
asked Sep 22 '16 at 12:07
Anonymous
214
214
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
well i think you are really close to the solution:
$$y'=-4y-3$$
Homogeneous part would be:
$$y'+ 4y = 0$$
which leads to:
$$y0=Ce^-4t$$
particular part would be (with initial assumption $yp=ax+b$):
$$yp=3/4$$
which leads to:
$$y(t)=Ce^-4t+3/4$$
$$limlimits_t to infty y(t)=3/4$$
answered Sep 22 '16 at 12:46
arash javan
1306
Is it y' = -4y - 3 or y' = 4y - 3
– Anonymous
Sep 22 '16 at 13:03
y'= -4y-3 try to solve some similar equations.
– arash javan
Sep 22 '16 at 13:07
@Anonymous mark the answer plz, if it was your solution
– arash javan
Sep 23 '16 at 14:09
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
well i think you are really close to the solution:
$$y'=-4y-3$$
Homogeneous part would be:
$$y'+ 4y = 0$$
which leads to:
$$y0=Ce^-4t$$
particular part would be (with initial assumption $yp=ax+b$):
$$yp=3/4$$
which leads to:
$$y(t)=Ce^-4t+3/4$$
$$limlimits_t to infty y(t)=3/4$$
answered Sep 22 '16 at 12:46
arash javan
1306
Is it y' = -4y - 3 or y' = 4y - 3
– Anonymous
Sep 22 '16 at 13:03
y'= -4y-3 try to solve some similar equations.
– arash javan
Sep 22 '16 at 13:07
@Anonymous mark the answer plz, if it was your solution
– arash javan
Sep 23 '16 at 14:09
add a comment |Â
up vote
0
down vote
well i think you are really close to the solution:
$$y'=-4y-3$$
Homogeneous part would be:
$$y'+ 4y = 0$$
which leads to:
$$y0=Ce^-4t$$
particular part would be (with initial assumption $yp=ax+b$):
$$yp=3/4$$
which leads to:
$$y(t)=Ce^-4t+3/4$$
$$limlimits_t to infty y(t)=3/4$$
answered Sep 22 '16 at 12:46
arash javan
1306
Is it y' = -4y - 3 or y' = 4y - 3
– Anonymous
Sep 22 '16 at 13:03
y'= -4y-3 try to solve some similar equations.
– arash javan
Sep 22 '16 at 13:07
@Anonymous mark the answer plz, if it was your solution
– arash javan
Sep 23 '16 at 14:09
add a comment |Â
up vote
0
down vote
up vote
0
down vote
well i think you are really close to the solution:
$$y'=-4y-3$$
Homogeneous part would be:
$$y'+ 4y = 0$$
which leads to:
$$y0=Ce^-4t$$
particular part would be (with initial assumption $yp=ax+b$):
$$yp=3/4$$
which leads to:
$$y(t)=Ce^-4t+3/4$$
$$limlimits_t to infty y(t)=3/4$$
answered Sep 22 '16 at 12:46
arash javan
1306
well i think you are really close to the solution:
$$y'=-4y-3$$
Homogeneous part would be:
$$y'+ 4y = 0$$
which leads to:
$$y0=Ce^-4t$$
particular part would be (with initial assumption $yp=ax+b$):
$$yp=3/4$$
which leads to:
$$y(t)=Ce^-4t+3/4$$
$$limlimits_t to infty y(t)=3/4$$
answered Sep 22 '16 at 12:46
arash javan
1306
edited Sep 22 '16 at 13:00
answered Sep 22 '16 at 12:46
arash javan
1306
answered Sep 22 '16 at 12:46
arash javan
1306
answered Sep 22 '16 at 12:46
arash javan
1306
1306
Is it y' = -4y - 3 or y' = 4y - 3
– Anonymous
Sep 22 '16 at 13:03
y'= -4y-3 try to solve some similar equations.
– arash javan
Sep 22 '16 at 13:07
@Anonymous mark the answer plz, if it was your solution
– arash javan
Sep 23 '16 at 14:09
add a comment |Â
Is it y' = -4y - 3 or y' = 4y - 3
– Anonymous
Sep 22 '16 at 13:03
y'= -4y-3 try to solve some similar equations.
– arash javan
Sep 22 '16 at 13:07
@Anonymous mark the answer plz, if it was your solution
– arash javan
Sep 23 '16 at 14:09
Is it y' = -4y - 3 or y' = 4y - 3
– Anonymous
Sep 22 '16 at 13:03
Is it y' = -4y - 3 or y' = 4y - 3
– Anonymous
Sep 22 '16 at 13:03
y'= -4y-3 try to solve some similar equations.
– arash javan
Sep 22 '16 at 13:07
y'= -4y-3 try to solve some similar equations.
– arash javan
Sep 22 '16 at 13:07
@Anonymous mark the answer plz, if it was your solution
– arash javan
Sep 23 '16 at 14:09
@Anonymous mark the answer plz, if it was your solution
– arash javan
Sep 23 '16 at 14:09
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1936963%2fwrite-a-differential-equation-fracdydt-ayb-whose-solutions-have-the%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
