Solve a differential algebraic equation

How-to 4 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

dae = {x'[t] - y[t] == 0, x[t] + 2y[t] == 0}

Output

{-y[t] + Derivative[1][x][t] == 0, x[t] + 2*y[t] == 0}

Step 2

DSolve[dae, {x[t], y[t]}, t]

Output

DSolve[{-y[t] + Derivative[1][x][t] == 0, x[t] + 2*y[t] == 0}, {x[t], y[t]}, t]

Step 3

dae2 = {x''[t] == y[t], x[t] + y[t] == 0, x[Pi] == 1, x'[Pi] == 0}

Output

{Derivative[2][x][t] == y[t], x[t] + y[t] == 0, x[Pi] == 1, Derivative[1][x][Pi] == 0}

Step 4

DSolve[dae2, {x[t], y[t]}, t]

Output

DSolve[{Derivative[2][x][t] == y[t], x[t] + y[t] == 0, x[Pi] == 1, Derivative[1][x][Pi] == 0}, {x[t], y[t]}, t]

Functions used

Solve a differential algebraic equation