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Beliebt Rechnen >

y^{''}-4y=t\H(t-3),y(0)=0,y^'(0)=5

Lösung

y^{^{''}} - 4 y = t H (t - 3), y (0) = 0, y^{^{'}} (0) = 5

Lösung

y = \frac{- 4 t + 20 e ^{2 t} - 20 e ^{- 2 t} + 5 e ^{- 2 (t - 3)} + 7 e ^{2 (t - 3)}}{16}

Schritte zur Lösung

y^{''} (t) - 4 y = t H (t - 3)

Solve using Laplace transform:

y = \frac{- 4 t + 20 e ^{2 t} - 20 e ^{- 2 t} + 5 e ^{- 2 (t - 3)} + 7 e ^{2 (t - 3)}}{16}

y = \frac{- 4 t + 20 e ^{2 t} - 20 e ^{- 2 t} + 5 e ^{- 2 (t - 3)} + 7 e ^{2 (t - 3)}}{16}

Graph

Beliebte Beispiele

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

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

x^{''}+2x^'+1x=e^{-2t},x(0)=2,x^'(0)=1

x^{^{''}} + 2 x^{^{'}} + 1 x = e^{- 2 t}, x (0) = 2, x^{^{'}} (0) = 1

y^{''}+4y=cos(2x)+1

y^{^{''}} + 4 y = cos (2 x) + 1

(d^2y)/(dx^2)+y=4xcos(x)

\frac{d ^{2} y}{d x ^{2}} + y = 4 x cos (x)

y^{^{''}} + 49 y = 3