Section 1.4 Exact ODE

Most of the solutions in this section are implicit.  They are not suitable to be solved by the DSolve command. However, we can show the implicit solution curve easily by using the ContourPlot command.

ContourPlot[Sin[x+y]+y^3 + y^2,{x,-3,6},{y,-1,1},Contours->10,ContourLabels->All]

ContourPlot[Cos [y] Cosh[x]+x,{x,0,3},{y,0,3},Contours->20,ContourLabels->All]

ContourPlot[Exp[x] + x y + Exp[-y],{x,-3,3},{y,-3,3},Contours->20,ContourLabels->All,Axes->True,ContourShading->None]