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Beliebt Rechnen >

y^{''}+6y^'+9y=t^{-2}e^{-3t}

Lösung

y^{^{''}} + 6 y^{^{'}} + 9 y = t^{- 2} e^{- 3 t}

Lösung

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

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 9 y = t^{- 2} e^{- 3 t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^'= 3/((x+2)^2)

y^{^{'}} = \frac{3}{( x + 2 ) ^{2}}

derivative 7^{x+arccos(x)}

d er i v a t i v e 7^{x + a r c c o s (x)}

integral from pi/5 to infinity of 5/x

\int_{\frac{π}{5}}^{\infty} \frac{5}{x} d x

f^{^{'}} (x) = \frac{3}{x}

integral of 1/(1+ln(x))

\int \frac{1}{1 + ln ( x )} d x