Given this differential equation: y'[x] + y[x] == a Sin[x],
which of the following Mathematica inputs defines the solution[x] as a function of x and correctly determines the integration constant by applying a specified boundary condition?
Note: several options are actually valid Mathematica inputs. Treat any option which returns a list and or transformation rule as incorrect for this problem.

Question

Given this differential equation: y'[x] + y[x] == a Sin[x], 
 which of the following Mathematica inputs defines the solution[x] as a function of x and correctly determines the integration constant by applying a specified boundary condition?  
 Note: several options are actually valid Mathematica inputs.   Treat any option which returns a list and or transformation rule as incorrect for this problem.

Accepted Answer

solution[x_] := y[X] /. DSolve[{y'[X] + y[X] == a Sin[X], y[0] == -a/2}, y[X], X][[1]]/.X->x

Answer

Solution[x_] := DSolve[{y'[X] + y[X] == a Sin[X]}, y[X], X]  /.C[1]->1/.X->x

Answer

solution[x] = DSolve[{y'[x_] + y[x_] == a Sin[x_], y[0] == -a⁄2}, y[x_], x_ ]

Answer

solution[x_] := DSolve[y'[X] + y[X] == a Sin[X], y[X], X]/.X->x

Crowdly

Given this differential equation: y'[x] + y[x] == a Sin[x], which of the follo...

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