︠07b37c73-4ec4-413a-8552-3607bf8136d1ai︠
%hide
%auto
#import os
x = var('x')
y = function('y', x)
@interact
def _(f=input_box(default=y+x-1),x0=input_box(default=0.0), y0=input_box(default=1.0)):
    #x = var('x')
    #y = function('y', x)
    g = function('g',x,y)
    g = f
    #y' = y + x - 1
    #x0 = 1.0
    #y0 = 2.0
    ff = desolve(diff(y,x) - f, y, ics=[x0,y0]) 
    # show([ff, plot(ff)])
    show(ff)
    show(plot(ff,(x,x0-1, x0+3)))
︡e5004ec3-946b-46ca-8718-8deab795424b︡{"html": "\n        <div padding=6 id=\"div-interact-52\">\n          <table width=800px height=20px bgcolor=\"#c5c5c5\" cellpadding=15>\n            <tr>\n              <td bgcolor=\"#f9f9f9\" valign=top align=left>\n            <table>\n              <tr><td colspan=3><table><tr><td align=right><font color=\"black\">f&nbsp;</font></td><td><input type=\"text\" value=\"x + y(x) - 1\" size=80 onchange=\"interact(52, {variable: 'f', adapt_number: 1, value: encode64(this.value)}, 1)\"></input></td>\n</tr><tr><td align=right><font color=\"black\">x0&nbsp;</font></td><td><input type=\"text\" value=\"0.000000000000000\" size=80 onchange=\"interact(52, {variable: 'x0', adapt_number: 2, value: encode64(this.value)}, 1)\"></input></td>\n</tr><tr><td align=right><font color=\"black\">y0&nbsp;</font></td><td><input type=\"text\" value=\"1.00000000000000\" size=80 onchange=\"interact(52, {variable: 'y0', adapt_number: 3, value: encode64(this.value)}, 1)\"></input></td>\n</tr></table></td></tr>\n              <tr><td></td><td style='width: 100%;'>\n        <div id=\"cell-interact-52\"><?__SAGE__START>\n          <table border=0 bgcolor=\"white\" width=100%>\n            <tr>\n              <td bgcolor=\"white\" align=left valign=top>\n                <pre><?__SAGE__TEXT></pre>\n              </td>\n            </tr>\n            <tr>\n              <td align=left valign=top><?__SAGE__HTML></td>\n            </tr>\n          </table><?__SAGE__END>\n        </div></td><td></td></tr>\n              <tr><td colspan=3></td></tr>\n            </table></td>\n            </tr>\n          </table>\n        </div>"}︡
︠4f4215c2-e460-4480-8118-66e9db266988︠
simplify(ff)
︡643abec6-2d1b-49f9-b20a-ce9b6c739431︡{"stdout": "-x + 25632/23225*e^x"}︡
︠84e791bc-cd53-487b-b5a4-06cac6a9b0fb︠
plot(ff)
︡9f60d011-de2b-4800-b69f-c877cdb4bd5b︡{"html": "<font color='black'><img src='cell://sage0.png'></font>"}︡

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