erweitern (x^2-81)y''(x)+(9-x)y'(x)+(x^2+18x+81)y

Lösung

erweitern

(x^{2} - 81) y^{''} (x) + (9 - x) y^{'} (x) + (x^{2} + 18 x + 81) y

x^{2} y'' (x) - 81 y'' (x) + 9 y' (x) - x y' (x) + x^{2} y + 18 x y + 81 y

Schritte zur Lösung

(x^{2} - 81) y^{''} (x) + (9 - x) y^{'} (x) + (x^{2} + 18 x + 81) y

Multipliziere aus

y^{''} (x) (x^{2} - 81) : x^{2} y^{''} (x) - 81 y^{''} (x)

= x^{2} y^{''} (x) - 81 y^{''} (x) + (9 - x) y^{'} (x) + (x^{2} + 18 x + 81) y

Multipliziere aus

y^{'} (x) (9 - x) : 9 y^{'} (x) - x y^{'} (x)

= x^{2} y^{''} (x) - 81 y^{''} (x) + 9 y^{'} (x) - x y^{'} (x) + (x^{2} + 18 x + 81) y

Multipliziere aus

y (x^{2} + 18 x + 81) : x^{2} y + 18 x y + 81 y

= x^{2} y^{''} (x) - 81 y^{''} (x) + 9 y^{'} (x) - x y^{'} (x) + x^{2} y + 18 x y + 81 y

s im pl i f y (3 + i)^{10}

e x p an d e^{x} (- e^{- x} x - e^{- x})

e x p an d \frac{( 6 - 3 x ) ^{2}}{4}

e x p an d \frac{s - 1}{( s + 2 ) ( s ^{2} + 4 )}

e x p an d \frac{2 ( x - 1 ) ^{2}}{( x - 2 ) ( x + 1 )}