Matematik differentialligning

Benyt separation og substitution.
Se evt her, modellen        y '  =  b - ay
http://www.matlex.dk/difflign.html

generelt:
                 differentialligningen
                                                      y ' = b - ay
                 har løsningen

                                                      y = C·e^-a·x + (b/a)
                                             

i anvendelse
              differentialligningen
                                                      dh/dt = 5,24 - 0,045·h
                 har løsningen

                                                      h(t) = C·e^-0,045·t + (5,24/0,045)

                                                      h(t) = C·e^-0,045·t + (1048/9)          gennem (0,50)

                                                      h(0) = C·e^-0,045·0 + (1048/9) = 50

                                                                 C + (1048/9) = 50

                                                                 C = (450-1048)/9 = -(598/9)
                 hvoraf
 
                                                      h(t) = -(66⁴/₉)·e^-0,045·t + (116⁴/₉)
                                       

                                             h(t) = -(598/9)·e^-0,045·t + (1048/9) = 100

                                                       -598·e^-0,045·t + 1048 = 900

                                                        598·e^-0,045·t = 1048-900 = 148

                                                        e^-0,045·t = (148/598) = (74/299)

                                                        e^0,045·t = (299/74)

                                                        0,045·t = ln(299/74)

                                                        t = ln(299/74) / 0,045