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Beliebt Rechnen >

(d^2y)/(dx^2)-(dy)/(dx)-6y=-e^x+12x

Lösung

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = - e^{x} + 12 x

Lösung

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} - 2 x + \frac{1}{3}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = - e^{x} + 12 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} - 2 x + \frac{1}{3}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} + \frac{1}{6} e^{x} - 2 x + \frac{1}{3}

Graph

Beliebte Beispiele

y^{''}+2y^'-3y=2cos(x)-4sin(x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 2 cos (x) - 4 sin (x)

1/2 y^{''}+2y=4tan(2t)-1/3 e^t

\frac{1}{2} y^{^{''}} + 2 y = 4 tan (2 t) - \frac{1}{3} e^{t}

38y^{''}-7y= 5/2

38 y^{^{''}} - 7 y = \frac{5}{2}

3y^{''}+12y=-4sin(3t)

3 y^{^{''}} + 12 y = - 4 sin (3 t)

y^{'''}+4y^'=3e^x(2x+5)

y^{^{'''}} + 4 y^{^{'}} = 3 e^{x} (2 x + 5)