Find the IVP solution to the following differential equationFinding the general solution of this differential...
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Find the IVP solution to the following differential equation
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Give the general solution to the following differential equation and use the general solution to solve this initial value problem:
$$y''-y=0,quad
y(1)=1+e,quad y'
(1)=-1+e,
quad y=e^{rt}$$
I found that the general solution is equal to
$$y(t)=C_1e^{-t} + C_2e^{t}$$
However I'm not sure how to find the solution to the initial value problem. I thought that $C_1=1$ and $C_2=-1$ might be the solution.
Thanks in advance for any help.
ordinary-differential-equations
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
asked Mar 13 at 16:25
user1user1
103
$endgroup$
add a comment |
$begingroup$
Give the general solution to the following differential equation and use the general solution to solve this initial value problem:
$$y''-y=0,quad
y(1)=1+e,quad y'
(1)=-1+e,
quad y=e^{rt}$$
I found that the general solution is equal to
$$y(t)=C_1e^{-t} + C_2e^{t}$$
However I'm not sure how to find the solution to the initial value problem. I thought that $C_1=1$ and $C_2=-1$ might be the solution.
Thanks in advance for any help.
ordinary-differential-equations
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
asked Mar 13 at 16:25
user1user1
103
$endgroup$
$begingroup$
Welcome to math.stackexchange. Please use MathJax when formatting your questions. math.meta.stackexchange.com/questions/5020/… On this exercise you should substitute the initial values into the solution. This gives two linear algebraic equations which you solve for $C_1$ and $C_2$.
$endgroup$
– John Wayland Bales
Mar 13 at 16:47
add a comment |
$begingroup$
Give the general solution to the following differential equation and use the general solution to solve this initial value problem:
$$y''-y=0,quad
y(1)=1+e,quad y'
(1)=-1+e,
quad y=e^{rt}$$
I found that the general solution is equal to
$$y(t)=C_1e^{-t} + C_2e^{t}$$
However I'm not sure how to find the solution to the initial value problem. I thought that $C_1=1$ and $C_2=-1$ might be the solution.
Thanks in advance for any help.
ordinary-differential-equations
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
asked Mar 13 at 16:25
user1user1
103
$endgroup$
Give the general solution to the following differential equation and use the general solution to solve this initial value problem:
$$y''-y=0,quad
y(1)=1+e,quad y'
(1)=-1+e,
quad y=e^{rt}$$
I found that the general solution is equal to
$$y(t)=C_1e^{-t} + C_2e^{t}$$
However I'm not sure how to find the solution to the initial value problem. I thought that $C_1=1$ and $C_2=-1$ might be the solution.
Thanks in advance for any help.
ordinary-differential-equations
ordinary-differential-equations
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
asked Mar 13 at 16:25
user1user1
103
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
asked Mar 13 at 16:25
user1user1
103
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
edited Mar 13 at 17:00
Rodrigo de Azevedo
13.2k41960
13.2k41960
asked Mar 13 at 16:25
user1user1
103
asked Mar 13 at 16:25
user1user1
103
asked Mar 13 at 16:25
user1user1
103
103
$begingroup$
Welcome to math.stackexchange. Please use MathJax when formatting your questions. math.meta.stackexchange.com/questions/5020/… On this exercise you should substitute the initial values into the solution. This gives two linear algebraic equations which you solve for $C_1$ and $C_2$.
$endgroup$
– John Wayland Bales
Mar 13 at 16:47
add a comment |
$begingroup$
Welcome to math.stackexchange. Please use MathJax when formatting your questions. math.meta.stackexchange.com/questions/5020/… On this exercise you should substitute the initial values into the solution. This gives two linear algebraic equations which you solve for $C_1$ and $C_2$.
$endgroup$
– John Wayland Bales
Mar 13 at 16:47
$begingroup$
Welcome to math.stackexchange. Please use MathJax when formatting your questions. math.meta.stackexchange.com/questions/5020/… On this exercise you should substitute the initial values into the solution. This gives two linear algebraic equations which you solve for $C_1$ and $C_2$.
$endgroup$
– John Wayland Bales
Mar 13 at 16:47
$begingroup$
Welcome to math.stackexchange. Please use MathJax when formatting your questions. math.meta.stackexchange.com/questions/5020/… On this exercise you should substitute the initial values into the solution. This gives two linear algebraic equations which you solve for $C_1$ and $C_2$.
$endgroup$
– John Wayland Bales
Mar 13 at 16:47
add a comment |
1 Answer
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Start with taking the derivative of your general solution and then plug in the respective initial values.
answered Mar 13 at 16:46
Maths2020Maths2020
385
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Was that helpful?
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– Maths2020
Mar 13 at 16:57
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$begingroup$
Start with taking the derivative of your general solution and then plug in the respective initial values.
answered Mar 13 at 16:46
Maths2020Maths2020
385
$endgroup$
$begingroup$
Was that helpful?
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– Maths2020
Mar 13 at 16:57
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$begingroup$
Start with taking the derivative of your general solution and then plug in the respective initial values.
answered Mar 13 at 16:46
Maths2020Maths2020
385
$endgroup$
$begingroup$
Was that helpful?
$endgroup$
– Maths2020
Mar 13 at 16:57
add a comment |
$begingroup$
Start with taking the derivative of your general solution and then plug in the respective initial values.
answered Mar 13 at 16:46
Maths2020Maths2020
385
$endgroup$
Start with taking the derivative of your general solution and then plug in the respective initial values.
answered Mar 13 at 16:46
Maths2020Maths2020
385
answered Mar 13 at 16:46
Maths2020Maths2020
385
answered Mar 13 at 16:46
Maths2020Maths2020
385
answered Mar 13 at 16:46
Maths2020Maths2020
385
385
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Was that helpful?
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– Maths2020
Mar 13 at 16:57
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– Maths2020
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$begingroup$
Welcome to math.stackexchange. Please use MathJax when formatting your questions. math.meta.stackexchange.com/questions/5020/… On this exercise you should substitute the initial values into the solution. This gives two linear algebraic equations which you solve for $C_1$ and $C_2$.
$endgroup$
– John Wayland Bales
Mar 13 at 16:47