python - Solve differential equation with SymPy -


i have following differential equation solve sympy

enter image description here

this differential equation has implicit solution (with h(0) = [0,1) , t = [0, inf) )

enter image description here

but sympy gives

enter image description here

which other packages such maxima able find. sympy unable, however. there way so? code is

import sympy sp sp.init_printing(use_unicode=true) h = sp.symbols('h', function=true) t = sp.symbols('t') eq = sp.eq(sp.derivative(h(t),t), (1 - h(t))**sp.rational(4,3) / h(t)) sp.dsolve(eq)

sympy leaves integral unevaluated because unsure sign of 1-y in integral.

the differential equation has singularity @ h=1, , behavior depends on side of 1 are. there isn't way h(t) < 1, 1 can substitute h(t) = 1 - g(t) g positive function: 

g = sp.symbols('g', function=true, positive=true) eq1 = eq.subs(h(t), 1 - g(t)) print(sp.dsolve(eq1))

this returns explicit solution of ode (actually 3 of them, sympy solves cubic equation). first 1 of looks reasonable.

eq(g(t), (-2*(c1 + t)/(sqrt(-8*(c1 + t)**3 + 729) + 27)**(1/3) - (sqrt(-8*(c1 + t)**3 + 729) + 27)**(1/3))**3/27)

Comments

Post a Comment

Popular posts from this blog

node.js - Node js - Trying to send POST request, but it is not loading javascript content -

i have been trying send post request website, , has not been loading full site. i guessing problem node js not loading javascript content, executing it. can see javascript in response, though never loads content javascript files producing in html. what mean is, doesn't execute javascript. how make node js code overcome this, , wait the full website load? have tried native code, , "request' module, both producing same errors. if helps, don't need native javascript. modules fine. some code have tried (request module): var options = { method: 'post', uri: 'https://url', formdata: { 'email': 'email', 'prize': '0', 'transactional': 'on' }, headers: { /* 'content-type': 'application/x-www-form-urlencoded' */ // set automatically } }; rp(options) .then(function (body) { console.log(body) }) .catch(function (err) { console.log(err) }); when fetch content...
Read more

javascript - Replicate keyboard event with html button -

i have tried few ways make happen. have javascript pinball game uses keyboard keys controls. converting application touch screen display. workaround, hoping overlay buttons when clicked simulate keyboard strokes. have done research , sounds should work. using jquery v3.2.1 here things have tried far... html element: <input type="button" class="coil"></input> $('.coil').trigger({type: 'keydown', which: 40, keycode: 40}); with this, not errors, nothing happens. var coilkey = $('body').keydown(function(e) { switch (e.keycode) { case 40: break;} }) $('.coil').click(coilkey); this 1 returns error in console... ((jquery.event.special[handleobj.origtype] || (intermediate value)).handle || handleobj.handler).apply not function below javascript game engine handles key listeners... addkeylistener: function (keyandlistener) { this.keylisteners.push(keyandlistener); }, // gi...
Read more

javascript - Web audio api 5.1 surround example not working in firefox -

i've been playing lott lately web audio api on both firefox , chrome. few days ago started experiment surround set. when trying surround audio in web audio api came notice example works fine in chrome v59 not in firefox v54. // create web audio api context var audioctx = new (window.audiocontext || window.webkitaudiocontext)(); audioctx.destination.channelinterpretation = 'discrete'; audioctx.destination.channelcountmode = 'explicit'; audioctx.destination.channelcount = 6; var oscillators = []; var merger = audioctx.createchannelmerger(6); console.log(audioctx.destination, merger); //merger.channelinterpretation = 'discrete'; //merger.channelcountmode = 'explicit'; //merger.channelcount = 6; var addoscilator = function(channel, frequency) { var oscillator = audioctx.createoscillator(); oscillator.frequency.value = frequency; // value in hertz oscillator.connect(merger,0,channel); oscillator.start(); oscillators.push(o...
Read more