Second order differential equation - analytical solution for $frac {d^2x}{dt^2} =frac{A}{f(t)}-B$.
-2
How to find the analytical solution for the following second-order differential equation?
$$frac {d^2x}{dt^2} =frac{A}{f(t)}-B$$
where $f(t)=C t$; $A$, $B$ and $C$ are constants.
differential-equations
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
asked Dec 10 '18 at 12:57
Harish
72
add a comment |
-2
How to find the analytical solution for the following second-order differential equation?
$$frac {d^2x}{dt^2} =frac{A}{f(t)}-B$$
where $f(t)=C t$; $A$, $B$ and $C$ are constants.
differential-equations
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
asked Dec 10 '18 at 12:57
Harish
72
4
Just integrate twice with respect to $t$?
– Hans Lundmark
Dec 10 '18 at 13:01
@HansLundmark, So the answer is $frac{BCt^2+2Atln{t}-2At}{2C}$
– Dhamnekar Winod
Dec 10 '18 at 13:18
That seems right, except for a missing minus sign in front of $BC t^2$.
– Hans Lundmark
Dec 10 '18 at 13:24
@DhamnekarWinod And integrating constants?
– Nosrati
Dec 10 '18 at 13:44
add a comment |
-2
-2
-2
How to find the analytical solution for the following second-order differential equation?
$$frac {d^2x}{dt^2} =frac{A}{f(t)}-B$$
where $f(t)=C t$; $A$, $B$ and $C$ are constants.
differential-equations
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
asked Dec 10 '18 at 12:57
Harish
72
How to find the analytical solution for the following second-order differential equation?
$$frac {d^2x}{dt^2} =frac{A}{f(t)}-B$$
where $f(t)=C t$; $A$, $B$ and $C$ are constants.
differential-equations
differential-equations
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
asked Dec 10 '18 at 12:57
Harish
72
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
asked Dec 10 '18 at 12:57
Harish
72
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
edited Dec 10 '18 at 13:08
Nosrati
26.5k62353
26.5k62353
asked Dec 10 '18 at 12:57
Harish
72
asked Dec 10 '18 at 12:57
Harish
72
asked Dec 10 '18 at 12:57
Harish
72
72
4
Just integrate twice with respect to $t$?
– Hans Lundmark
Dec 10 '18 at 13:01
@HansLundmark, So the answer is $frac{BCt^2+2Atln{t}-2At}{2C}$
– Dhamnekar Winod
Dec 10 '18 at 13:18
That seems right, except for a missing minus sign in front of $BC t^2$.
– Hans Lundmark
Dec 10 '18 at 13:24
@DhamnekarWinod And integrating constants?
– Nosrati
Dec 10 '18 at 13:44
add a comment |
4
Just integrate twice with respect to $t$?
– Hans Lundmark
Dec 10 '18 at 13:01
@HansLundmark, So the answer is $frac{BCt^2+2Atln{t}-2At}{2C}$
– Dhamnekar Winod
Dec 10 '18 at 13:18
That seems right, except for a missing minus sign in front of $BC t^2$.
– Hans Lundmark
Dec 10 '18 at 13:24
@DhamnekarWinod And integrating constants?
– Nosrati
Dec 10 '18 at 13:44
4
4
Just integrate twice with respect to $t$?
– Hans Lundmark
Dec 10 '18 at 13:01
Just integrate twice with respect to $t$?
– Hans Lundmark
Dec 10 '18 at 13:01
@HansLundmark, So the answer is $frac{BCt^2+2Atln{t}-2At}{2C}$
– Dhamnekar Winod
Dec 10 '18 at 13:18
@HansLundmark, So the answer is $frac{BCt^2+2Atln{t}-2At}{2C}$
– Dhamnekar Winod
Dec 10 '18 at 13:18
That seems right, except for a missing minus sign in front of $BC t^2$.
– Hans Lundmark
Dec 10 '18 at 13:24
That seems right, except for a missing minus sign in front of $BC t^2$.
– Hans Lundmark
Dec 10 '18 at 13:24
@DhamnekarWinod And integrating constants?
– Nosrati
Dec 10 '18 at 13:44
@DhamnekarWinod And integrating constants?
– Nosrati
Dec 10 '18 at 13:44
add a comment |
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4
Just integrate twice with respect to $t$?
– Hans Lundmark
Dec 10 '18 at 13:01
@HansLundmark, So the answer is $frac{BCt^2+2Atln{t}-2At}{2C}$
– Dhamnekar Winod
Dec 10 '18 at 13:18
That seems right, except for a missing minus sign in front of $BC t^2$.
– Hans Lundmark
Dec 10 '18 at 13:24
@DhamnekarWinod And integrating constants?
– Nosrati
Dec 10 '18 at 13:44