Directly Obtain Solution Expressions for ODEs 

Directly obtain an expression for the solution of an ODE using DSolveValue.

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X sol = DSolveValue[{Derivative[1][y][x] + y[x] == a Sin[x], y[0] == 0}, y[x], x]

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Plot the solution.

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X Plot[Evaluate[Table[sol, {a, 7}]], {x, 0, 4 \[Pi]}]

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Compute the derivative of the solution for an ODE.

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X DSolveValue[{(y^\[Prime]\[Prime])[x] + y[x] == 0, y[0] == 0, Derivative[1][y][0] == 1}, Derivative[1][y][x], x]

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Solve for arbitrary expressions involving the dependent variables.

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X DSolveValue[{Derivative[1][y][x] == x y[x], Derivative[1][z][x] == 5 z[x], y[0] == 3, z[0] == 5}, y[x], x]

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X DSolveValue[{Derivative[1][y][x] == x y[x], Derivative[1][z][x] == 5 z[x], y[0] == 3, z[0] == 5}, y[x] + z[1], x]

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X DSolveValue[{Derivative[1][y][x] == x y[x], Derivative[1][z][x] == 5 z[x], y[0] == 3, z[0] == 5}, \!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(7\)]\(\(( \*SuperscriptBox[\(y[x]\), \(2\)] + 3\ z[x])\) \[DifferentialD]x\)\), x]

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Obtain a pure function solution for a nonlinear second-order ODE.

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X eqn = {(y^\[Prime]\[Prime])[x] == 4 Derivative[1][y][x] + 1/Derivative[1][y][x]^2, y[1] == 3, Derivative[1][y][1] == 1};

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X sol = DSolveValue[eqn, y, x]

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Verify the solution.

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X eqn /. {y -> sol} // FullSimplify

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