de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

(y^{^{''}}) - 2 y^{^{'}} + y = \frac{e ^{x}}{1 + x ^{2}}

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

Schritte zur Lösung

(y^{''} (x)) - 2 y^{'} (x) + y = \frac{e ^{x}}{1 + x ^{2}}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{1}{2} e^{x} ln (1 + x^{2}) + e^{x} x arctan (x)

Graph

Beliebte Beispiele

y^{''}+2y^'+2y=t^2

y^{^{''}} + 2 y^{^{'}} + 2 y = t^{2}

y^{''}-2y^'+y=e-2x

y^{^{''}} - 2 y^{^{'}} + y = e - 2 x

y^{''}+4y^'+6y=1^{-t}

y^{^{''}} + 4 y^{^{'}} + 6 y = 1^{- t}

y^{''}+y=t-pi/2 ,y(pi/2)=0,y^'(pi/2)=1

y^{^{''}} + y = t - \frac{π}{2}, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 1

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

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