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Beliebt Rechnen >

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

Lösung

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{t ^{3}}

Lösung

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t}}{2 t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t}}{2 t}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{e ^{t}}{2 t}

Graph

Beliebte Beispiele

y^{''}+2y^'=3xe^x

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

y^{''}-2y^'-3y=3

y^{^{''}} - 2 y^{^{'}} - 3 y = 3

y^{'''}+4y^{''}+5y^'+2y=10cos(t)

y^{^{'''}} + 4 y^{^{''}} + 5 y^{^{'}} + 2 y = 10 cos (t)

(D^3-D^2+D-1)y=4sin(x)

(D^{3} - D^{2} + D - 1) y = 4 sin (x)

y^{''}-2y^'-8y=18te^{4t}

y^{^{''}} - 2 y^{^{'}} - 8 y = 18 t e^{4 t}