Mixing
System of differential equations from a given solution
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I am having trouble giving an example of a system of differential equations for which (t, 1) is a solution. From what I understand, if (t,1) is a solution, then $x''(t) = alpha t + beta$ but I am unsure of how to explicitly describe a system given this information. Any hints would be greatly appreciated!
ordinary-differential-equations
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
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I am having trouble giving an example of a system of differential equations for which (t, 1) is a solution. From what I understand, if (t,1) is a solution, then $x''(t) = alpha t + beta$ but I am unsure of how to explicitly describe a system given this information. Any hints would be greatly appreciated!
ordinary-differential-equations
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
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In a system of equations there is necessarily more than one equation. In this case there are two ordinary differential equations of the form $x_1' = f_1(t,x_1,x_2)$ and $x_2' = f_2(t,x_1,x_2)$. Just plug in the given solutions $(x_1(t),x_2(t)) = (t,1)$ to obtain functions $f_1, f_2$.
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– Christoph
Jan 23 at 7:48
add a comment |
$begingroup$
I am having trouble giving an example of a system of differential equations for which (t, 1) is a solution. From what I understand, if (t,1) is a solution, then $x''(t) = alpha t + beta$ but I am unsure of how to explicitly describe a system given this information. Any hints would be greatly appreciated!
ordinary-differential-equations
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
$endgroup$
I am having trouble giving an example of a system of differential equations for which (t, 1) is a solution. From what I understand, if (t,1) is a solution, then $x''(t) = alpha t + beta$ but I am unsure of how to explicitly describe a system given this information. Any hints would be greatly appreciated!
ordinary-differential-equations
ordinary-differential-equations
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
asked Jan 23 at 7:08
Richard VillalobosRichard Villalobos
1807
1807
$begingroup$
In a system of equations there is necessarily more than one equation. In this case there are two ordinary differential equations of the form $x_1' = f_1(t,x_1,x_2)$ and $x_2' = f_2(t,x_1,x_2)$. Just plug in the given solutions $(x_1(t),x_2(t)) = (t,1)$ to obtain functions $f_1, f_2$.
$endgroup$
– Christoph
Jan 23 at 7:48
add a comment |
$begingroup$
In a system of equations there is necessarily more than one equation. In this case there are two ordinary differential equations of the form $x_1' = f_1(t,x_1,x_2)$ and $x_2' = f_2(t,x_1,x_2)$. Just plug in the given solutions $(x_1(t),x_2(t)) = (t,1)$ to obtain functions $f_1, f_2$.
$endgroup$
– Christoph
Jan 23 at 7:48
$begingroup$
In a system of equations there is necessarily more than one equation. In this case there are two ordinary differential equations of the form $x_1' = f_1(t,x_1,x_2)$ and $x_2' = f_2(t,x_1,x_2)$. Just plug in the given solutions $(x_1(t),x_2(t)) = (t,1)$ to obtain functions $f_1, f_2$.
$endgroup$
– Christoph
Jan 23 at 7:48
$begingroup$
In a system of equations there is necessarily more than one equation. In this case there are two ordinary differential equations of the form $x_1' = f_1(t,x_1,x_2)$ and $x_2' = f_2(t,x_1,x_2)$. Just plug in the given solutions $(x_1(t),x_2(t)) = (t,1)$ to obtain functions $f_1, f_2$.
$endgroup$
– Christoph
Jan 23 at 7:48
add a comment |
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$begingroup$
In a system of equations there is necessarily more than one equation. In this case there are two ordinary differential equations of the form $x_1' = f_1(t,x_1,x_2)$ and $x_2' = f_2(t,x_1,x_2)$. Just plug in the given solutions $(x_1(t),x_2(t)) = (t,1)$ to obtain functions $f_1, f_2$.
$endgroup$
– Christoph
Jan 23 at 7:48