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Beliebt Rechnen >

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

Lösung

linear

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^{''}-2y^'-3y=4ex-6

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e x - 6

y^{''}-2y^'-3y=4ex-3

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e x - 3

y^{''}+k^2y=e^{2t},y(0)=0,y^'(0)=0

y^{^{''}} + k^{2} y = e^{2 t}, y (0) = 0, y^{^{'}} (0) = 0

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

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

y^{''}+2y^'-3y=-9cos(2x)-33sin(2x)

y^{^{''}} + 2 y^{^{'}} - 3 y = - 9 cos (2 x) - 33 sin (2 x)