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Beliebt Rechnen >

(d^2y)/(dx^2)+derivative of 8y+65y=100

Lösung

\frac{d ^{2} y}{d x ^{2}} + \frac{d}{d x} (8 y) + 65 y = 100

Lösung

y = e^{- 4 x} (c_{1} cos (7 x) + c_{2} sin (7 x)) + \frac{20}{13}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + \frac{d}{d x} (8 y) + 65 y = 100

Solve linear ODE:

y = e^{- 4 x} (c_{1} cos (7 x) + c_{2} sin (7 x)) + \frac{20}{13}

y = e^{- 4 x} (c_{1} cos (7 x) + c_{2} sin (7 x)) + \frac{20}{13}

Graph

Beliebte Beispiele

y^{''}+2y^'-15y=-5x^2+3x-3

y^{^{''}} + 2 y^{^{'}} - 15 y = - 5 x^{2} + 3 x - 3

y^{''}+2y^'+37y=4\H(t)

y^{^{''}} + 2 y^{^{'}} + 37 y = 4 H (t)

5y^{''}+4y^'+8y=4x-1

5 y^{^{''}} + 4 y^{^{'}} + 8 y = 4 x - 1

4y^{''}+20y^'+169y=e^{2t}

4 y^{^{''}} + 20 y^{^{'}} + 169 y = e^{2 t}

(D^3+8)y=x^4+2x+1

(D^{3} + 8) y = x^{4} + 2 x + 1