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Beliebt Rechnen >

y^{''}+4y=cos(t),y^'(0)=1,y(0)=1

Lösung

y^{^{''}} + 4 y = cos (t), y^{^{'}} (0) = 1, y (0) = 1

Lösung

y = \frac{2}{3} cos (2 t) + \frac{1}{2} sin (2 t) + \frac{1}{3} cos (t)

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{2}{3} cos (2 t) + \frac{1}{2} sin (2 t) + \frac{1}{3} cos (t)

y = \frac{2}{3} cos (2 t) + \frac{1}{2} sin (2 t) + \frac{1}{3} cos (t)

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+(dy)/(dx)=tan(2x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = tan (2 x)

49y^{''}+140y^'+136=0

49 y^{^{''}} + 140 y^{^{'}} + 136 = 0

y^{''}+y=2cos(x),y(0)=1

y^{^{''}} + y = 2 cos (x), y (0) = 1

y^{'''}+y^'=t^2+1

y^{^{'''}} + y^{^{'}} = t^{2} + 1

y^{^{''}} - 2 y + 2 = 0