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Beliebt Rechnen >

(d^2y)/(dx^2)-6(dy)/(dx)+8y=4e^{3x}+8x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 4 e^{3 x} + 8 x

Lösung

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 4 e^{3 x} + 8 x

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

y^{'''}-2y^{''}+y^'=3cos(2t)

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 3 cos (2 t)

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

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

y^{''}+13y=7e^{3x}

y^{^{''}} + 13 y = 7 e^{3 x}

y^{''}+4y^'+3y=-19te^{4t}

y^{^{''}} + 4 y^{^{'}} + 3 y = - 19 t e^{4 t}