DE with boundary values
system:sage

{{{id=0|
var('x')
@interact
def BCs(b=input_box(1,label='BC at far endpoint'), c = slider(1,5,step_size = .01), a = 1): 
    P1 = text("$y''+y=0,\ y(0) = a,\ y(b) = c$",(4,-1/(c-3.14152)))
    P2 = plot(a*cos(x)+(b-a*cos(c))*sin(x)/sin(c),x,0,5)
    (P1+P2).show()
///

<html><!--notruncate--><div padding=6 id='div-interact-0'> <table width=800px height=20px bgcolor='#c5c5c5'
                 cellpadding=15><tr><td bgcolor='#f9f9f9' valign=top align=left><table><tr><td align=right><font color="black">BC at far endpoint&nbsp;</font></td><td><input type='text' value="1" size=80 onchange='interact(0, "sage.server.notebook.interact.update(0, \"b\", 38, sage.server.notebook.interact.standard_b64decode(\""+encode64(this.value)+"\"), globals());sage.server.notebook.interact.recompute(0)")'></input></td></tr>
<tr><td align=right><font color="black">c&nbsp;</font></td><td><table><tr><td>
        <div id='slider-c-0' class='ui-slider ui-slider-3' style='margin:0px;'><span class='ui-slider-handle'></span></div>
        </td><td><font color='black' id='slider-c-0-lbl'></font></td></tr></table><script>(function(){ var values = 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setTimeout(function() {
    $('#slider-c-0').slider({
        stepping: 1, min: 0, max: 400, startValue: 0,
        change: function (e,ui) { var position = ui.value; if(values!=null) $('#slider-c-0-lbl').text(values[position]); interact(0, "sage.server.notebook.interact.update(0, \"c\", 39, sage.server.notebook.interact.standard_b64decode(\""+encode64(position)+"\"), globals());sage.server.notebook.interact.recompute(0)"); },
        slide: function(e,ui) { if(values!=null) $('#slider-c-0-lbl').text(values[ui.value]); }
    });
    if(values != null) $('#slider-c-0-lbl').text(values[$('#slider-c-0').slider('value')]);
    }, 1); })();</script></td></tr>
<tr><td align=right><font color="black">a&nbsp;</font></td><td><input type='text' value="1" size=80 onchange='interact(0, "sage.server.notebook.interact.update(0, \"a\", 40, sage.server.notebook.interact.standard_b64decode(\""+encode64(this.value)+"\"), globals());sage.server.notebook.interact.recompute(0)")'></input></td></tr>
</table><div id='cell-interact-0'><?__SAGE__START>
        <table border=0 bgcolor='#white' width=100% height=100%>
        <tr><td bgcolor=white align=left valign=top><pre><?__SAGE__TEXT></pre></td></tr>
        <tr><td  align=left valign=top><?__SAGE__HTML></td></tr>
        </table><?__SAGE__END></div></td>
                 </tr></table></div>
                 </html>
}}}

{{{id=1|

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}}}

{{{id=2|

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{{{id=4|

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}}}