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Beliebt Rechnen >

y^{''}-3y^'-4y=t^2

Lösung

y^{^{''}} - 3 y^{^{'}} - 4 y = t^{2}

Lösung

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{t ^{2}}{4} + \frac{3 t}{8} - \frac{13}{32}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) - 4 y = t^{2}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{t ^{2}}{4} + \frac{3 t}{8} - \frac{13}{32}

y = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{t ^{2}}{4} + \frac{3 t}{8} - \frac{13}{32}

Graph

Beliebte Beispiele

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

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

x^{''}-x^'-6x=5t

x^{^{''}} - x^{^{'}} - 6 x = 5 t

y^{''}-2y^'-3y=8e^{-t}

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{- t}

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

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

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

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