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Beliebt Rechnen >

(D^2+4D+5)y=e^{(-x)}+15x

Lösung

(D^{2} + 4 D + 5) y = e^{(- x)} + 15 x

Lösung

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{2} e^{- x} + 3 x - \frac{12}{5}

Schritte zur Lösung

(D^{2} + 4 D + 5) y = e^{- x} + 15 x

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{2} e^{- x} + 3 x - \frac{12}{5}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{1}{2} e^{- x} + 3 x - \frac{12}{5}

Graph

Beliebte Beispiele

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

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

(D^2+1)y=cos^2(x)

(D^{2} + 1) y = cos^{2} (x)

(d^2y)/(dx^2)+6(dy)/(dx)+9y=xe^{-3x}

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 9 y = x e^{- 3 x}

y^{''}-y=t,y(0)=0,y^'(0)=0

y^{^{''}} - y = t, y (0) = 0, y^{^{'}} (0) = 0

y^{''}-y=t,y(0)=0,y^'(0)=1

y^{^{''}} - y = t, y (0) = 0, y^{^{'}} (0) = 1