de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

y^{''}+4y^'-5y=te^t,y(0)=1,y^'(0)=0

Lösung

y^{^{''}} + 4 y^{^{'}} - 5 y = t e^{t}, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = (1 - \frac{35}{216}) e^{t} + \frac{35}{216} e^{- 5 t} + \frac{e ^{t} t ^{2}}{12} - \frac{e ^{t} t}{36}

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) - 5 y = t e^{t}

Solve linear ODE:

y = (1 - \frac{35}{216}) e^{t} + \frac{35}{216} e^{- 5 t} + \frac{e ^{t} t ^{2}}{12} - \frac{e ^{t} t}{36}

y = (1 - \frac{35}{216}) e^{t} + \frac{35}{216} e^{- 5 t} + \frac{e ^{t} t ^{2}}{12} - \frac{e ^{t} t}{36}

Graph

Beliebte Beispiele

y^{''}-4y^'-12y=x-6

y^{^{''}} - 4 y^{^{'}} - 12 y = x - 6

x^{''}+x=cos(3t)

x^{^{''}} + x = cos (3 t)

y^{'''}-5y^{''}+6y^'=5+4sin(x)

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 5 + 4 sin (x)

y^{''}+2y^'-4y=8x^2

y^{^{''}} + 2 y^{^{'}} - 4 y = 8 x^{2}

8y^{''}-32y=16cos(x)

8 y^{^{''}} - 32 y = 16 cos (x)