de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

y^{''}-6y^'+9y=e^3x,y(0)=-1,y^'(0)=1

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3} x, y (0) = - 1, y^{^{'}} (0) = 1

Lösung

y = (- 1 - \frac{2 e ^{3}}{27}) e^{3 x} + (1 - \frac{- e ^{3} - 27}{9}) x e^{3 x} + \frac{e ^{3} x}{9} + \frac{2 e ^{3}}{27}

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 9 y = e^{3} x

Solve linear ODE:

y = (- 1 - \frac{2 e ^{3}}{27}) e^{3 x} + (1 - \frac{- e ^{3} - 27}{9}) x e^{3 x} + \frac{e ^{3} x}{9} + \frac{2 e ^{3}}{27}

y = (- 1 - \frac{2 e ^{3}}{27}) e^{3 x} + (1 - \frac{- e ^{3} - 27}{9}) x e^{3 x} + \frac{e ^{3} x}{9} + \frac{2 e ^{3}}{27}

Graph

Beliebte Beispiele

(d^2y)/(dt^2)-5(dy)/(dt)+6=0

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 = 0

-5y^{''}-2y^'+24=0

- 5 y^{^{''}} - 2 y^{^{'}} + 24 = 0

linear 1/4 y^{''}+4y=tan(4t)-1/3 e^{3t}

l in e a r \frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{3} e^{3 t}

2y^{'''}-2y^'=-3t^2-4t

2 y^{^{'''}} - 2 y^{^{'}} = - 3 t^{2} - 4 t

y^{'''}-2y^{''}+y^'=3t^2-18

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 3 t^{2} - 18