de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{t} (\frac{4}{5} cos (t) - \frac{2}{5} sin (t)) - \frac{2}{5} sin (t) + \frac{1}{5} cos (t)

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + 2 y = cos (t)

Solve linear ODE:

y = e^{t} (\frac{4}{5} cos (t) - \frac{2}{5} sin (t)) - \frac{2}{5} sin (t) + \frac{1}{5} cos (t)

y = e^{t} (\frac{4}{5} cos (t) - \frac{2}{5} sin (t)) - \frac{2}{5} sin (t) + \frac{1}{5} cos (t)

Graph

Beliebte Beispiele

derivative of (2x^3/3-8x-5)

\frac{d}{d x} (\frac{2 x ^{3}}{3} - 8 x - 5)

derivative of (54/x)

\frac{d}{d x} (\frac{54}{x})

limit as x approaches 0 of 5x-6

x \to 0 lim (5 x - 6)

tangent sin(3x)+cos(8x)

t an g e n t sin (3 x) + cos (8 x)

vereinfachen 1/3 x^6(x^2-3)

s im pl i f y \frac{1}{3} x^{6} (x^{2} - 3)