direction field with initial data for E&P2 1.3.25, which has an edge to its domain of validity at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYsNiVRInhGJ0Y0RjdGKw==QyQtSSV3aXRoRzYiNiNJKERFdG9vbHNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUhIiI=PkklZGVxMUc2Ii8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJDYjSSJ4R0YkRi0tSSVzcXJ0RzYkRihJKF9zeXNsaWJHRiQ2IywmRi0iIiJGKiEiIg==LUknREVwbG90RzYiNiZJJWRlcTFHRiQtSSJ5R0YkNiNJInhHRiQvRio7ISIkIiIkL0YoRiw=Some intial data points:QyQ+SSZpbml0c0c2IjYkNyQiIiMiIiE3JCIiIkYpRis=LUknREVwbG90RzYiNidJJWRlcTFHRiQtSSJ5R0YkNiNJInhHRiQvRio7ISIkIiIkL0YoRiw8I0kmaW5pdHNHRiQ=Initial data to the left of the 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 isocline solution which separates the two kinds of solutions will abort MAPLE in the plotting routine because those solutions must hit the trouble at the edge of the domain of the DE.optional advanced discussionThe "general" solution cannot be solved for either variable:Pkkkc29sRzYiLUknZHNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiRJJWRlcTFHRiQtSSJ5R0YkNiNJInhHRiQ=But we can find real values of the constant by plugging in an initial data point:QyQ+SSlzb2xfaW5pdEc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQtSSVzdWJzR0YpNiUvLUkieUdGJTYjSSJ4R0YlIiIhL0YzIiIjSSIlR0YlSSRfQzFHRiUiIiI=LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiNJIiVHNiI=This only works for initial data to the right of the same isocline solution unless we combine the three logarithm terms into a single one by hand using rules of logarithms and the difference of squares factorization, which allows us to get a real value of the constant:QyQ+SSVzb2wyRzYiLywqSSJ4R0YlIiIiKiQsJkYoRiktSSJ5R0YlNiNGKCEiIiNGKSIiI0YxLUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyokLCZGL0YpRipGKUYxRilJJF9DMUdGJUYvIiIhRik=QyQ+SSpzb2wyX2luaXRHNiItSSZzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUklc3Vic0dGKTYlLy1JInlHRiU2I0kieEdGJSIiIy9GM0Y0SSIlR0YlSSRfQzFHRiUiIiI=PkkjQzFHNiItSSZldmFsZkclKnByb3RlY3RlZEc2I0kiJUdGJA==We substitute that value into the implicit solution and then implicitplot it:QyQ+SSZjdXJ2ZUc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiUvSSRfQzFHRiVJI0MxR0YlLy1JInlHRiU2I0kieEdGJUYvSSVzb2wyR0YlIiIiQyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJnBsb3RzR0YlISIiQyQtSS1pbXBsaWNpdHBsb3RHNiI2KEkmY3VydmVHRiUvSSJ4R0YlOyEiJCIiJC9JInlHRiVGKi9JJWdyaWRHRiU3JCIkKyJGMi9JKnRoaWNrbmVzc0dGJSIiIy9JJmNvbG9yR0YlSSVibHVlR0YlIiIiPkkpZXhhY3Rzb2xHNiJJIiVHRiQ=Now we display the directionfield together with this exact solution, which contains two disjoint pieces, unlike a numerical solution which can only consist of one continuous curve (since the numerical solution follows its nose from the initial data point in both directions along a solution curve):QyQ+SSZpbml0c0c2IjYkNyQiIiMiIiE3JCIiIkYpRis=QyQtSSdERXBsb3RHNiI2J0klZGVxMUdGJS1JInlHRiU2I0kieEdGJS9GKzshIiQiIiQvRilGLTwjSSZpbml0c0dGJSIiIg==QyQ+SStkZmllbGRwbG90RzYiSSIlR0YlIiIiLUkoZGlzcGxheUc2IjYkSStkZmllbGRwbG90R0YkSSlleGFjdHNvbEdGJA==JSFH