教學共 8 個步驟，在同一個工作階段中依序執行。每一步都在引擎上實際執行過，下方的輸出就是它產生的結果。

步驟 1

DSolveValue[y'[x] + y[x] == a Sin[x], y[x], x]

輸出

C[1]/E^x + (a*(-Cos[x] + Sin[x]))/2

步驟 2

sol = DSolveValue[{y'[x] + y[x] == a Sin[x], y[0] == 0}, y, x]

輸出

Function[{x}, a/(2*E^x) + (a*(-Cos[x] + Sin[x]))/2]

步驟 3

{y'[x] + y[x] == a Sin[x], y[0] == 0} /. y -> sol//Simplify

輸出

{(a/E^x + 2*Derivative[1, Function[{x}, a/(2*E^x) + (a*(-Cos[x] + Sin[x]))/2], x] - a*Cos[x] + a*Sin[x])/2 == a*Sin[x], True}

步驟 4

Plot[Table[sol[x] /. {a -> i}, {i, 7}], {x, -2, 10}]

輸出

-Graphics-

步驟 5

DSolveValue[{y''[x] + y[x] == 0, y[0] == 0, y'[0] == 1}, y[3], x]

輸出

DSolveValue[{y[x] + Derivative[2][y][x] == 0, y[0] == 0, Derivative[1][y][0] == 1}, y[3], x]

步驟 6

DSolveValue[{y''[x] + y[x] == 0, y[0] == 0, y'[0] == 1}, y'[x], x]

輸出

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

步驟 7

DSolveValue[{y'[x] + y[x] == Sin[x], y'[0] ^ 2 == 1}, y[x], x]

輸出

DSolveValue[{y[x] + Derivative[1][y][x] == Sin[x], Derivative[1][y][0]^2 == 1}, y[x], x]

步驟 8

DSolve[{y'[x] + y[x] == Sin[x], y'[0] ^ 2 == 1}, y[x], x]

輸出

DSolve[{y[x] + Derivative[1][y][x] == Sin[x], Derivative[1][y][0]^2 == 1}, y[x], x]

D solve working with d solve working with dsolvevalue

使用到的函式