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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{2 e ^{t} t ^{2} ln ( t ) - 3 e ^{t} t ^{2}}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{2 e ^{t} t ^{2} ln ( t ) - 3 e ^{t} t ^{2}}{4}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{2 e ^{t} t ^{2} ln ( t ) - 3 e ^{t} t ^{2}}{4}

Graph

Beliebte Beispiele

y^{''}+16y^'+64y=t^{-2}e^{-8t}

y^{^{''}} + 16 y^{^{'}} + 64 y = t^{- 2} e^{- 8 t}

y^{''}+6y^'+9y=e^{3x}+2

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{3 x} + 2

y^{''}+4y=tsin^2(t)

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

y^{''}-2y^'-15=0

y^{^{''}} - 2 y^{^{'}} - 15 = 0

(D^2-3D+2)y=xe^x

(D^{2} - 3 D + 2) y = x e^{x}