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Beliebt Rechnen >

(d^2y)/(dt^2)-3(dy)/(dt)-18y=(t+1)e^t

Lösung

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 18 y = (t + 1) e^{t}

Lösung

y = c_{1} e^{6 t} + c_{2} e^{- 3 t} - \frac{e ^{t} t}{20} - \frac{19}{400} e^{t}

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} - 3 \frac{d y}{d t} - 18 y = (t + 1) e^{t}

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 3 t} - \frac{e ^{t} t}{20} - \frac{19}{400} e^{t}

y = c_{1} e^{6 t} + c_{2} e^{- 3 t} - \frac{e ^{t} t}{20} - \frac{19}{400} e^{t}

Graph

Beliebte Beispiele

y^{^{''}} + y = H (t)

y^{''}-2y^'+5y=104sin(3x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 104 sin (3 x)

x^{''}+2x^'+5x=4t^2

x^{^{''}} + 2 x^{^{'}} + 5 x = 4 t^{2}

y^{''}-y^'-2y=1-x

y^{^{''}} - y^{^{'}} - 2 y = 1 - x

y^{'''}-5y^{''}+6y^'=3+7x

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 3 + 7 x