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Beliebt Rechnen >

y^{''}-8y^'+16y=-5e^{4x}+(e^{4x})/x

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = - 5 e^{4 x} + \frac{e ^{4 x}}{x}

Lösung

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{- 5 e ^{4 x} x ^{2} - 2 e ^{4 x} x + 2 e ^{4 x} x ln ( x )}{2}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 16 y = - 5 e^{4 x} + \frac{e ^{4 x}}{x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{- 5 e ^{4 x} x ^{2} - 2 e ^{4 x} x + 2 e ^{4 x} x ln ( x )}{2}

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + \frac{- 5 e ^{4 x} x ^{2} - 2 e ^{4 x} x + 2 e ^{4 x} x ln ( x )}{2}

Graph

Beliebte Beispiele

ay^{''}+by^'+cy=g(t)

a y^{^{''}} + b y^{^{'}} + cy = g (t)

(d^{2} - 4) y = 2 x

y^{''}+y^'-2y=2t-40cos(2t)

y^{^{''}} + y^{^{'}} - 2 y = 2 t - 40 cos (2 t)

y^{''}-6y^'+45y=-4sin(2t)

y^{^{''}} - 6 y^{^{'}} + 45 y = - 4 sin (2 t)

y^{''}+16y=sin(x)

y^{^{''}} + 16 y = sin (x)