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Beliebt Rechnen >

(d^2y)/(dt^2)+8(dy)/(dt)+15y=3

Lösung

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} + 15 y = 3

Lösung

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{1}{5}

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} + 15 y = 3

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{1}{5}

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{1}{5}

Graph

Beliebte Beispiele

y^{''}-6y^'-27y=-57t+54t^2

y^{^{''}} - 6 y^{^{'}} - 27 y = - 57 t + 54 t^{2}

y^{''}+15y^'+56y=112x^2+60x+4+72e^x

y^{^{''}} + 15 y^{^{'}} + 56 y = 112 x^{2} + 60 x + 4 + 72 e^{x}

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

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

y^{''}+16y=0.5sin(4t),y(0)=0.5

y^{^{''}} + 16 y = 0.5 sin (4 t), y (0) = 0.5

(D^2+9)y=81x^2+(14cos(x))

(D^{2} + 9) y = 81 x^{2} + (14 cos (x))