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Beliebt Rechnen >

linear y^{''}-2y^'+5y=6e^t,y(0)=0

Lösung

linear

y^{^{''}} - 2 y^{^{'}} + 5 y = 6 e^{t}, y (0) = 0

Lösung

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

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + 5 y = 6 e^{t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+3y^'+2y=10u,y(0)=0,y^'(0)=0

y^{^{''}} + 3 y^{^{'}} + 2 y = 10 u, y (0) = 0, y^{^{'}} (0) = 0

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

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

(d^2y)/(dx^2)-y-6=1

\frac{d ^{2} y}{d x ^{2}} - y - 6 = 1

y^{''}+y^'+2y=x+3,y(0)=0,y^'(0)=1

y^{^{''}} + y^{^{'}} + 2 y = x + 3, y (0) = 0, y^{^{'}} (0) = 1

y^{''}+y^'+4.25=0

y^{^{''}} + y^{^{'}} + 4.25 = 0