Further Examples: DSolve (modified)

Here is the solution to a second order ordinary differential equation. It uses C[1] and C[2] as the constants of integration by default.

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This solves the same equation, specifying that the integration constants are K[1] and K[2].

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You can add constraints and boundary conditions for differential equations.

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This verifies the solution.

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Here is the solution for a Riccati-type equation.

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Here is the solution for an Abel-type equation.

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Here is the solution for a more general Abel-type equation. K$ variables are used as dummy integration variables.

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Here is an equation whose solution involves Mathieu functions.

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Solving this equation uses a combination of methods for rational, exponential, and special function solutions, as well as reduction of order.

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For this equation, DSolve returns an implicit solution.

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The solution of this equation involves products of Airy functions.

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When the initial or boundary conditions are given at singularities, DSolve uses Limit internally.

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This equation has missing variables.

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The arguments of the dependent variable in differential equations should match the independent variables literally.

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