# Plotting the Solution

A plot of the solution given by DSolve can give useful information about the nature of the solution, for instance, whether it is oscillatory in nature. It can also serve as a means of solution verification if the shape of the graph is known from theory or from plotting the vector field associated with the differential equation. A few examples that use different *Mathematica* graphics functions follow.

Here is the general solution to a linear first-order equation.

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The solution can be plotted for specific values of the constant

C[1] using

Plot. The use of

Evaluate reduces the time taken by

Plot and can also help in cases where the solution has discontinuities.

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Here is the plot for a linear second-order ODE with initial values prescribed at 0.

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This nonlinear equation has two solutions that can be plotted on the same graph.

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The solution to this Abel ODE is given in implicit form.

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A contour plot can be used to study the nature of the solution. Each contour line corresponds to a solution to the ODE for a fixed value of

C[1].

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Here is the plot of the solutions to a system of two linear ODEs. The

WorkingPrecision option in

Plot is required because the solution is fairly complicated.

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The

ParametricPlot function can be used to trace the solution curve

in the plane.

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Here is the plot for the solution to a DAE.

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Here is the general solution to a linear PDE.

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Here is a plot of the solution surface for a particular choice of the arbitrary function

C[1].

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