{"version":9,"randomSeed":"d11efe48e19f313bdbe1042ef194aebb","graph":{"viewport":{"xmin":-0.4697965939948763,"ymin":-0.35350085788411434,"xmax":13.431533734678347,"ymax":8.27119774744061}},"expressions":{"list":[{"type":"text","id":"66","text":"inspired by \"A very interesting differential equation.\" by Michael Penn (2020) https://www.youtube.com/watch?v=rNUfiQgj6ZI"},{"type":"expression","id":"1","color":"#c74440","latex":"f\\left(x\\right)=ax^{b}"},{"type":"expression","id":"2","color":"#2d70b3","latex":"a=\\left(\\frac{1}{2}+\\frac{\\sqrt{5}}{2}\\right)^{\\frac{1}{2}-\\frac{\\sqrt{5}}{2}}"},{"type":"expression","id":"3","color":"#388c46","latex":"b=\\frac{1+\\sqrt{5}}{2}"},{"type":"expression","id":"4","color":"#6042a6","latex":"y=f'\\left(x\\right)"},{"type":"expression","id":"7","color":"#2d70b3","latex":"abx^{b-1}"},{"type":"expression","id":"5","color":"#000000","latex":"x=f\\left(y\\right)"},{"type":"expression","id":"8","color":"#388c46","latex":"\\sqrt[b]{\\frac{x}{a}}"},{"type":"expression","id":"10","color":"#000000","latex":"a^{-\\frac{1}{b}}x^{\\frac{1}{b}}"},{"type":"text","id":"26","text":"equations that lead to the solution"},{"type":"expression","id":"23","color":"#388c46","latex":"\\frac{1}{b}=b-1"},{"type":"expression","id":"24","color":"#6042a6","latex":"a^{-\\frac{1}{b}}=ab"}]}}