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en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 24 Apr 2017 19:12:47 GMTMon, 24 Apr 2017 19:12:47 GMTThe latest questions and posts added to MaplePrimeshttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Newest Questions and Posts
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differential equations with user defined function
http://www.mapleprimes.com/questions/221757-Differential-Equations-With-User-Defined-Function?ref=Feed:MaplePrimes:New%20Questions%20&%20Posts
<p>I would like to solve the following differential equation with a relatively complicated function that is best declared.</p>
<p>myfun := proc (x::float)</p>
<p>local output;</p>
<p>output := 4*x^2;</p>
<p>end proc;</p>
<p><br>
de := diff(y(x), x)+myfun(x)*y(x) = 0.;</p>
<p>However, this gives the following message:</p>
<p>Error, invalid input: myfun expects its 1st argument, x, to be of type float, but received x</p>
<p>Any suggestions?</p>
<p> </p>
<p> </p>
<p>I would like to solve the following differential equation with a relatively complicated function that is best declared.</p>
<p>myfun := proc (x::float)</p>
<p>local output;</p>
<p>output := 4*x^2;</p>
<p>end proc;</p>
<p><br>
de := diff(y(x), x)+myfun(x)*y(x) = 0.;</p>
<p>However, this gives the following message:</p>
<p>Error, invalid input: myfun expects its 1st argument, x, to be of type float, but received x</p>
<p>Any suggestions?</p>
<p> </p>
<p> </p>
221757Mon, 24 Apr 2017 13:43:29 ZmikemesonmikemesonFind the set of solutions of each of the linear congruence:
http://www.mapleprimes.com/questions/221755-Find-The-Set-Of-Solutions-Of-Each-Of?ref=Feed:MaplePrimes:New%20Questions%20&%20Posts
<p>Find the set of solutions of each of the linear congruence:</p>
<p><strong>a)</strong> x≡3x≡3 (mod 5).</p>
<p><strong>b)</strong> 2x≡52x≡5 (mod 9).</p>
<p>Find the set of solutions of each of the linear congruence:</p>
<p><strong>a)</strong> x≡3x≡3 (mod 5).</p>
<p><strong>b)</strong> 2x≡52x≡5 (mod 9).</p>
221755Mon, 24 Apr 2017 10:02:15 Zjojo2jojo2How to use Select
http://www.mapleprimes.com/questions/221754-How-To-Use-Select?ref=Feed:MaplePrimes:New%20Questions%20&%20Posts
<p>Experts.</p>
<p>In view of the worksheet:</p>
<p><a href="/view.aspx?sf=221754_question/VRP_permute.mw">VRP_permute.mw</a></p>
<p>What I need is<br>
a) a better way to display the Tour_Distances (from 1 to M) and<br>
b) a way to select tour elements where each component is <= to a specified distance (say <=H) and the corresponding tour(s) (from Tour2).<br>
</p>
<p>Experts.</p>
<p>In view of the worksheet:</p>
<p><a href="/view.aspx?sf=221754_question/VRP_permute.mw">VRP_permute.mw</a></p>
<p>What I need is<br>
a) a better way to display the Tour_Distances (from 1 to M) and<br>
b) a way to select tour elements where each component is <= to a specified distance (say <=H) and the corresponding tour(s) (from Tour2).<br>
</p>
221754Mon, 24 Apr 2017 09:19:30 Zbrian bovrilbrian bovrilHow to solve Laplace transformations of systems of differential equations
http://www.mapleprimes.com/questions/221752-How-To-Solve-Laplace-Transformations?ref=Feed:MaplePrimes:New%20Questions%20&%20Posts
<p>My question is: <strong>Use the laplace transform to solve the system.</strong></p>
<p>dx/dt + d^2y/dt^2 = 5e^(2t)</p>
<p>dx/dt - x - dy/dt + y = 8e^(2t)</p>
<p>x(0) = 2, y(0) = 1, y'(0) = 1</p>
<p><strong>What I've done in Maple:</strong></p>
<p>with(inttrans);<br>
with(DEtools);<br>
eq5 := (diff(x(t), t)+diff(y(t), t$2) = 5*exp(2*t), t, s);</p>
<p>eq5s := laplace(%, t, s);</p>
<p>eq6 := (diff(x(t), t)-x-(diff(y(t), t))+y = 8*exp(2*t), t, s);</p>
<p>eq6s := laplace(%, t, s);</p>
<p>solve({eq5s, eq6s}, {laplace(x(t), t, s), laplace(y(t), t, s)});</p>
<p>subs({x(0) = 2, y(0) = 1, (D(y))(0) = 1}, %);</p>
<p>eq3 := invlaplace(%, s, t);</p>
<p>How do I simplify? If you plug it into maple I come up with an answer that has x and y on each side. I guess I'm just wondering how I can set them equal to each other to solve and get rid of the variable x and y. I know answer is correct as I've also ran it through ODEtest. Please help.</p>
<p>However you figure out getting rid of the variables I assume will help me also in solving the next problem:</p>
<p><strong>Use the Laplace Transform to solve the system</strong></p>
<p>dx/dt = 7x - y + 6z</p>
<p>dy/dt = -10x + 4y - 12z</p>
<p>dz/dt = -2x + y - z</p>
<p>x(0) = 5, y(0) = 7, z(0) = 2</p>
<p>I have attempted the second problem much like the first. Thank you for your time.</p>
<p>My question is: <strong>Use the laplace transform to solve the system.</strong></p>
<p>dx/dt + d^2y/dt^2 = 5e^(2t)</p>
<p>dx/dt - x - dy/dt + y = 8e^(2t)</p>
<p>x(0) = 2, y(0) = 1, y'(0) = 1</p>
<p><strong>What I've done in Maple:</strong></p>
<p>with(inttrans);<br />
with(DEtools);<br />
eq5 := (diff(x(t), t)+diff(y(t), t$2) = 5*exp(2*t), t, s);</p>
<p>eq5s := laplace(%, t, s);</p>
<p>eq6 := (diff(x(t), t)-x-(diff(y(t), t))+y = 8*exp(2*t), t, s);</p>
<p>eq6s := laplace(%, t, s);</p>
<p>solve({eq5s, eq6s}, {laplace(x(t), t, s), laplace(y(t), t, s)});</p>
<p>subs({x(0) = 2, y(0) = 1, (D(y))(0) = 1}, %);</p>
<p>eq3 := invlaplace(%, s, t);</p>
<p>How do I simplify? If you plug it into maple I come up with an answer that has x and y on each side. I guess I'm just wondering how I can set them equal to each other to solve and get rid of the variable x and y. I know answer is correct as I've also ran it through ODEtest. Please help.</p>
<p>However you figure out getting rid of the variables I assume will help me also in solving the next problem:</p>
<p><strong>Use the Laplace Transform to solve the system</strong></p>
<p>dx/dt = 7x - y + 6z</p>
<p>dy/dt = -10x + 4y - 12z</p>
<p>dz/dt = -2x + y - z</p>
<p>x(0) = 5, y(0) = 7, z(0) = 2</p>
<p>I have attempted the second problem much like the first. Thank you for your time.</p>
221752Sun, 23 Apr 2017 22:45:48 ZhmagiihmagiiHow to put the independent variable on the vertical axis
http://www.mapleprimes.com/questions/221751-How-To-Put-The-Independent-Variable?ref=Feed:MaplePrimes:New%20Questions%20&%20Posts
<p>Hi!</p>
<p>If somebody could help me it would be awesome!</p>
<p>I would like to be able to switch the independent variable onto the vertical axis!</p>
<p>If that is not possible, what i'm trying to do is modelise in a function a set of points, but with multiple values for the same x, but not more than one for the y, so the best option would be to switch the variables, to have x dependant of y. My graphic has to be vertical though, so I can't just switch the points.</p>
<p>Thank you a lot</p>
<p>Charlotte</p>
<p>Hi!</p>
<p>If somebody could help me it would be awesome!</p>
<p>I would like to be able to switch the independent variable onto the vertical axis!</p>
<p>If that is not possible, what i'm trying to do is modelise in a function a set of points, but with multiple values for the same x, but not more than one for the y, so the best option would be to switch the variables, to have x dependant of y. My graphic has to be vertical though, so I can't just switch the points.</p>
<p>Thank you a lot</p>
<p>Charlotte</p>
221751Sun, 23 Apr 2017 21:16:20 ZCharlotteCCCharlotteCCShorten fraction
http://www.mapleprimes.com/questions/221750-Shorten-Fraction?ref=Feed:MaplePrimes:New%20Questions%20&%20Posts
<p>I'm not sure if this is possible but I have a very accurate fraction, say something like 1,000 digits / 1,000 digits. What I'm wanting to do is effectively turn this into a fraction like 100 digits / 100 digits.</p>
<p>For example (on a much smaller scale) I have 151/11 and would like to turn this into 41/3 From 3 digits/2 digits to 2 digits/1 digits.</p>
<p>How would I do that?</p>
<p>Thanks</p>
<p>I'm not sure if this is possible but I have a very accurate fraction, say something like 1,000 digits / 1,000 digits. What I'm wanting to do is effectively turn this into a fraction like 100 digits / 100 digits.</p>
<p>For example (on a much smaller scale) I have 151/11 and would like to turn this into 41/3 From 3 digits/2 digits to 2 digits/1 digits.</p>
<p>How would I do that?</p>
<p>Thanks</p>
221750Sun, 23 Apr 2017 15:05:22 Zdc539dc539