Mixing
Finding an unknown function out of an DE (involving an integral and an inverse Laplacetransform)
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Well, I've the following problem for an unkown function $x(t)$:
$$x'(t)cdottext{a}+text{b}cdotfrac{x'(t)}{x(t)+text{c}}+frac{partial}{partial t}left{int_0^tx(tau)cdotmathcal{L}_text{s}^{-1}left{frac{1}{frac{1}{f+sl}+frac{s}{qs+p}}right}_{left(t-tauright)}spacetext{d}tauright}=0spaceLongleftrightarrowspace$$
$$x(t)=dotstag1$$
How can solve that differential equation. I have no idea or clue whatsoever.
The thing I also know is that, $x(0)=x'(0)=0$. The rest of the constants are real and positive.
integration ordinary-differential-equations laplace-transform mathematical-physics convolution
asked Jan 19 at 16:13
JanJan
21.9k31240
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add a comment |
$begingroup$
Well, I've the following problem for an unkown function $x(t)$:
$$x'(t)cdottext{a}+text{b}cdotfrac{x'(t)}{x(t)+text{c}}+frac{partial}{partial t}left{int_0^tx(tau)cdotmathcal{L}_text{s}^{-1}left{frac{1}{frac{1}{f+sl}+frac{s}{qs+p}}right}_{left(t-tauright)}spacetext{d}tauright}=0spaceLongleftrightarrowspace$$
$$x(t)=dotstag1$$
How can solve that differential equation. I have no idea or clue whatsoever.
The thing I also know is that, $x(0)=x'(0)=0$. The rest of the constants are real and positive.
integration ordinary-differential-equations laplace-transform mathematical-physics convolution
asked Jan 19 at 16:13
JanJan
21.9k31240
$endgroup$
$begingroup$
The partial derivative allows you to simplify the integral into x(t)*...
$endgroup$
– Peter Foreman
Jan 19 at 16:16
$begingroup$
@PeterForeman ohoke, but that does not solve the problem so I don't have to much about that.
$endgroup$
– Jan
Jan 19 at 17:51
add a comment |
$begingroup$
Well, I've the following problem for an unkown function $x(t)$:
$$x'(t)cdottext{a}+text{b}cdotfrac{x'(t)}{x(t)+text{c}}+frac{partial}{partial t}left{int_0^tx(tau)cdotmathcal{L}_text{s}^{-1}left{frac{1}{frac{1}{f+sl}+frac{s}{qs+p}}right}_{left(t-tauright)}spacetext{d}tauright}=0spaceLongleftrightarrowspace$$
$$x(t)=dotstag1$$
How can solve that differential equation. I have no idea or clue whatsoever.
The thing I also know is that, $x(0)=x'(0)=0$. The rest of the constants are real and positive.
integration ordinary-differential-equations laplace-transform mathematical-physics convolution
asked Jan 19 at 16:13
JanJan
21.9k31240
$endgroup$
Well, I've the following problem for an unkown function $x(t)$:
$$x'(t)cdottext{a}+text{b}cdotfrac{x'(t)}{x(t)+text{c}}+frac{partial}{partial t}left{int_0^tx(tau)cdotmathcal{L}_text{s}^{-1}left{frac{1}{frac{1}{f+sl}+frac{s}{qs+p}}right}_{left(t-tauright)}spacetext{d}tauright}=0spaceLongleftrightarrowspace$$
$$x(t)=dotstag1$$
How can solve that differential equation. I have no idea or clue whatsoever.
The thing I also know is that, $x(0)=x'(0)=0$. The rest of the constants are real and positive.
integration ordinary-differential-equations laplace-transform mathematical-physics convolution
integration ordinary-differential-equations laplace-transform mathematical-physics convolution
asked Jan 19 at 16:13
JanJan
21.9k31240
asked Jan 19 at 16:13
JanJan
21.9k31240
asked Jan 19 at 16:13
JanJan
21.9k31240
asked Jan 19 at 16:13
JanJan
21.9k31240
asked Jan 19 at 16:13
JanJan
21.9k31240
21.9k31240
$begingroup$
The partial derivative allows you to simplify the integral into x(t)*...
$endgroup$
– Peter Foreman
Jan 19 at 16:16
$begingroup$
@PeterForeman ohoke, but that does not solve the problem so I don't have to much about that.
$endgroup$
– Jan
Jan 19 at 17:51
add a comment |
$begingroup$
The partial derivative allows you to simplify the integral into x(t)*...
$endgroup$
– Peter Foreman
Jan 19 at 16:16
$begingroup$
@PeterForeman ohoke, but that does not solve the problem so I don't have to much about that.
$endgroup$
– Jan
Jan 19 at 17:51
$begingroup$
The partial derivative allows you to simplify the integral into x(t)*...
$endgroup$
– Peter Foreman
Jan 19 at 16:16
$begingroup$
The partial derivative allows you to simplify the integral into x(t)*...
$endgroup$
– Peter Foreman
Jan 19 at 16:16
$begingroup$
@PeterForeman ohoke, but that does not solve the problem so I don't have to much about that.
$endgroup$
– Jan
Jan 19 at 17:51
$begingroup$
@PeterForeman ohoke, but that does not solve the problem so I don't have to much about that.
$endgroup$
– Jan
Jan 19 at 17:51
add a comment |
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$begingroup$
The partial derivative allows you to simplify the integral into x(t)*...
$endgroup$
– Peter Foreman
Jan 19 at 16:16
$begingroup$
@PeterForeman ohoke, but that does not solve the problem so I don't have to much about that.
$endgroup$
– Jan
Jan 19 at 17:51