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Beliebt Rechnen >

y^{''}+16y=e^{-4t}+3sin(4t)

Lösung

y^{^{''}} + 16 y = e^{- 4 t} + 3 sin (4 t)

Lösung

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{32} e^{- 4 t} - \frac{3 t cos ( 4 t )}{8}

Schritte zur Lösung

y^{''} (t) + 16 y = e^{- 4 t} + 3 sin (4 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{32} e^{- 4 t} - \frac{3 t cos ( 4 t )}{8}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{32} e^{- 4 t} - \frac{3 t cos ( 4 t )}{8}

Graph

Beliebte Beispiele

y^{''}-4y=-6cos(4x)+2sin(4x)

y^{^{''}} - 4 y = - 6 cos (4 x) + 2 sin (4 x)

y^{''}+3y^'+2y= 1/((5+e^x))

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{( 5 + e ^{x} )}

y^{''}+4y=9,ty(0)=0,y^'(0)=0

y^{^{''}} + 4 y = 9, t y (0) = 0, y^{^{'}} (0) = 0

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

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

y^{''}-y^'-6y=e^{3t}+5t

y^{^{''}} - y^{^{'}} - 6 y = e^{3 t} + 5 t