de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

y^{''}+2y^'+5y=4e^{(-x)}-xcos(2x)

Lösung

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 e^{(- x)} - x cos (2 x)

Lösung

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + e^{- x} + \frac{- 4 x sin ( 2 x ) - x cos ( 2 x )}{17} + \frac{76}{289} sin (2 x) + \frac{2}{289} cos (2 x)

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 5 y = 4 e^{(- x)} - x cos (2 x)

Solve linear ODE:

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + e^{- x} + \frac{- 4 x sin ( 2 x ) - x cos ( 2 x )}{17} + \frac{76}{289} sin (2 x) + \frac{2}{289} cos (2 x)

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + e^{- x} + \frac{- 4 x sin ( 2 x ) - x cos ( 2 x )}{17} + \frac{76}{289} sin (2 x) + \frac{2}{289} cos (2 x)

Graph

Beliebte Beispiele

(D^2+1)y=sin(x)sin(2x)

(D^{2} + 1) y = sin (x) sin (2 x)

y^{''}+16y=sin(3x)

y^{^{''}} + 16 y = sin (3 x)

2x^{''}-x^'+3t=5

2 x^{^{''}} - x^{^{'}} + 3 t = 5

y^{''}-2y^'+82y=excos(9x)

y^{^{''}} - 2 y^{^{'}} + 82 y = e x cos (9 x)

y^{''}-9y^'+6y=xe^x

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