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Beliebt Rechnen >

x^{''}+x=sin^2(t)

Lösung

x^{^{''}} + x = sin^{2} (t)

Lösung

x = c_{1} cos (t) + c_{2} sin (t) + cos (t) (cos (t) - \frac{1}{3} cos^{3} (t)) + \frac{sin ^{4} ( t )}{3}

Schritte zur Lösung

x^{''} (t) + x = sin^{2} (t)

Solve linear ODE:

x = c_{1} cos (t) + c_{2} sin (t) + cos (t) (cos (t) - \frac{1}{3} cos^{3} (t)) + \frac{sin ^{4} ( t )}{3}

x = c_{1} cos (t) + c_{2} sin (t) + cos (t) (cos (t) - \frac{1}{3} cos^{3} (t)) + \frac{sin ^{4} ( t )}{3}

Graph

Beliebte Beispiele

y^{''}+3y^'+2y=e^{-x}

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- x}

x^{''}+10x^'+29x=te^{-t}

x^{^{''}} + 10 x^{^{'}} + 29 x = t e^{- t}

y^{'''}+3y^{''}+3y^'+y=e^{-x}

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = e^{- x}

x^{''}+36x=33cos(5t)

x^{^{''}} + 36 x = 33 cos (5 t)

(d^2y)/(dx^2)+4(dy)/(dx)-12y=24

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 y = 24