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Beliebt Rechnen >

y^{''}-2y+5y=1,+e^{-t}y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - 2 y + 5 y = 1, + e^{- t} y (0) = 0, y^{^{'}} (0) = 0

Lösung

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

Schritte zur Lösung

y^{''} (t) - 2 y + 5 y = 1

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+y=xcos(2x)

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

y^{''}+2y^'=x^2+3x^2e^{-2x}+e^{2x}+1

y^{^{''}} + 2 y^{^{'}} = x^{2} + 3 x^{2} e^{- 2 x} + e^{2 x} + 1

y^{''}-8y^'+12y=e^{2x}(x^2-1)

y^{^{''}} - 8 y^{^{'}} + 12 y = e^{2 x} (x^{2} - 1)

y^{''}+y^'-12y=2te-4t,y(0)=-5,y^'(0)=-4

y^{^{''}} + y^{^{'}} - 12 y = 2 t e - 4 t, y (0) = - 5, y^{^{'}} (0) = - 4

y^{''}+25y=5tan^2(5x)cos(5x)

y^{^{''}} + 25 y = 5 tan^{2} (5 x) cos (5 x)