y^{''}-2y^'+2y=3x+e^xtan(x)

Lösung

y^{^{''}} - 2 y^{^{'}} + 2 y = 3 x + e^{x} tan (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{x} cos (x) (\frac{3}{2} e^{- x} x cos (x) + \frac{3}{2} e^{- x} x sin (x) + \frac{3}{2} e^{- x} cos (x) - ln (tan (x) + sec (x)) + sin (x)) + e^{x} sin (x) \cdot \int \frac{cos ( x ) ( 3 x + e ^{x} tan ( x ) )}{e ^{x}} d x

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 2 y = 3 x + e^{x} tan (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{x} cos (x) (\frac{3}{2} e^{- x} x cos (x) + \frac{3}{2} e^{- x} x sin (x) + \frac{3}{2} e^{- x} cos (x) - ln (tan (x) + sec (x)) + sin (x)) + e^{x} sin (x) \cdot \int \frac{cos ( x ) ( 3 x + e ^{x} tan ( x ) )}{e ^{x}} d x

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{x} cos (x) (\frac{3}{2} e^{- x} x cos (x) + \frac{3}{2} e^{- x} x sin (x) + \frac{3}{2} e^{- x} cos (x) - ln (tan (x) + sec (x)) + sin (x)) + e^{x} sin (x) \cdot \int \frac{cos ( x ) ( 3 x + e ^{x} tan ( x ) )}{e ^{x}} d x

y^{^{''}} + y^{^{'}} - 2 y = ln (x)

y^{^{''}} - 12 y^{^{'}} + 36 y = 4 e^{6 x}

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t), y (0) = 1, y (0) = 0

x^{^{''}} - 25 x = 3 e^{2 t}

(D^{3} + 3 D^{2} - 4) y = x e^{- 2 x}