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Beliebt Rechnen >

y^{''}+6y=t^4,y(0)=0,y^'(0)=0

Lösung

y^{^{''}} + 6 y = t^{4}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = \frac{t ^{4}}{6} - \frac{t ^{2}}{3} - \frac{1}{9} cos (6 t) + \frac{1}{9}

Schritte zur Lösung

y^{''} (t) + 6 y = t^{4}

Solve linear ODE:

y = \frac{t ^{4}}{6} - \frac{t ^{2}}{3} - \frac{1}{9} cos (6 t) + \frac{1}{9}

y = \frac{t ^{4}}{6} - \frac{t ^{2}}{3} - \frac{1}{9} cos (6 t) + \frac{1}{9}

Graph

Beliebte Beispiele

(D^2+2D-8)y=(6x^{-1}-x^{-2})e^{2x}

(D^{2} + 2 D - 8) y = (6 x^{- 1} - x^{- 2}) e^{2 x}

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

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

y^{''}-y=5,e^{-4x}+2xy(0)=0

y^{^{''}} - y = 5, e^{- 4 x} + 2 x y (0) = 0

y^{''}-y^'-2y=2xe^{-x}+xsin(x)

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

36y^{''}-y=(xe^x)/6

36 y^{^{''}} - y = \frac{x e ^{x}}{6}