erweitern y''(x)+(x-1)^2y'(x)-4(x-1)y

Lösung

erweitern

y^{''} (x) + (x - 1)^{2} y^{'} (x) - 4 (x - 1) y

y'' (x) + x^{2} y' (x) - 2 x y' (x) + y' (x) - 4 x y + 4 y

Schritte zur Lösung

y^{''} (x) + (x - 1)^{2} y^{'} (x) - 4 (x - 1) y

Multipliziere aus

- 4 y (x - 1) : - 4 x y + 4 y

= y^{''} (x) + (x - 1)^{2} y^{'} (x) - 4 x y + 4 y

Vereinfache

y^{''} (x) + (x - 1)^{2} y^{'} (x) - 4 x y + 4 y : y^{''} (x) + x^{2} y^{'} (x) - 2 x y^{'} (x) + y^{'} (x) - 4 x y + 4 y

= y^{''} (x) + x^{2} y^{'} (x) - 2 x y^{'} (x) + y^{'} (x) - 4 x y + 4 y

e x p an d (2 x - y = H (x, y)) d H (x, y)

e x p an d \frac{( 16 - x ) ^{2} x}{32}

e x p an d (1 + cos (x))^{4} \cdot sin (x)

e x p an d \frac{1}{10} (e^{x} - e^{- x})

s im pl i f y x^{3} δ (x - 2)