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Beliebt Rechnen >

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

Lösung

y^{^{''}} - 2 y^{^{'}} + y = \frac{3 e ^{t}}{t ^{2} + 1}

Lösung

y = c_{1} e^{t} + c_{2} t e^{t} - \frac{3}{2} e^{t} ln (t^{2} + 1) + 3 e^{t} t arctan (t)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} - \frac{3}{2} e^{t} ln (t^{2} + 1) + 3 e^{t} t arctan (t)

y = c_{1} e^{t} + c_{2} t e^{t} - \frac{3}{2} e^{t} ln (t^{2} + 1) + 3 e^{t} t arctan (t)

Graph

Beliebte Beispiele

(d^2y)/(dt^2)+2(dy)/(dt)+4y=13t^3

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 4 y = 13 t^{3}

y^{''}+y^'-12y=e^x+e^2

y^{^{''}} + y^{^{'}} - 12 y = e^{x} + e^{2}

5 y^{^{''}} + y^{^{'}} = 6 x

y^{''}-8y^'+17y=e^{4x}-x^2

y^{^{''}} - 8 y^{^{'}} + 17 y = e^{4 x} - x^{2}

y^{''}-81y=e^{10}t

y^{^{''}} - 81 y = e^{10} t