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Beliebt Rechnen >

y^{''}+ay^'=e^{3t}

Lösung

y^{^{''}} + a y^{^{'}} = e^{3 t}

Lösung

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

Schritte zur Lösung

y^{''} (t) + a y^{'} (t) = e^{3 t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

4y^{''}-11y^'-3y=5e^{3x}

4 y^{^{''}} - 11 y^{^{'}} - 3 y = 5 e^{3 x}

linear y^{''}-3y^'+2y=e^x

l in e a r y^{^{''}} - 3 y^{^{'}} + 2 y = e^{x}

y^{''}-y^'+y=(2e^{3t}+5t)^7

y^{^{''}} - y^{^{'}} + y = (2 e^{3 t} + 5 t)^{7}

(d^2y)/(dx^2)-9(dy)/(dx)+5y=xe^x

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 5 y = x e^{x}

y^{''}+4y^'+4y=e^{-t},y(0)=0,y^'(0)=1

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1