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Beliebt Rechnen >

y^{''}+2y^'+2y=1+cos(sqrt(2)t)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+4y^'+7t=t^3e^{4t}cos(t)

y^{^{''}} + 4 y^{^{'}} + 7 t = t^{3} e^{4 t} cos (t)

(d^2y)/(dx^2)-y=sin^2(x)

\frac{d ^{2} y}{d x ^{2}} - y = sin^{2} (x)

y^{''}-2y^'+26y=excos(5x)

y^{^{''}} - 2 y^{^{'}} + 26 y = e x cos (5 x)

y^{''}-2y^'-3y=(12e^{4x})/(1+e^{2x)}

y^{^{''}} - 2 y^{^{'}} - 3 y = \frac{12 e ^{4 x}}{1 + e ^{2 x}}

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

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