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Beliebt Rechnen >

(d^2y)/(dx^2)+(dy)/(dx)-12y=xe^{2x}

Lösung

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

Lösung

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{e ^{2 x} x}{6} - \frac{5}{36} e^{2 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{e ^{2 x} x}{6} - \frac{5}{36} e^{2 x}

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{e ^{2 x} x}{6} - \frac{5}{36} e^{2 x}

Graph

Beliebte Beispiele

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

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

y^{''}-5y^'+6y=3e^{3x}+36x^2

y^{^{''}} - 5 y^{^{'}} + 6 y = 3 e^{3 x} + 36 x^{2}

x^{''}+16x=8sin(2t)

x^{^{''}} + 16 x = 8 sin (2 t)

y^{'''}-3y^'-2y=2x+1

y^{^{'''}} - 3 y^{^{'}} - 2 y = 2 x + 1

y^{'''}-2y^{''}-4y^'+8y=e^{2x}

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = e^{2 x}