y^{''}+12y^'+24y=4381e^{2x}cos(13x)

Lösung

y^{^{''}} + 12 y^{^{'}} + 24 y = 4381 e^{2 x} cos (13 x)

y = c_{1} e^{2 (3 - 3) x} + c_{2} e^{- 2 (3 + 3) x} + 16 e^{2 x} sin (13 x) - 9 e^{2 x} cos (13 x)

Schritte zur Lösung

y^{''} (x) + 12 y^{'} (x) + 24 y = 4381 e^{2 x} cos (13 x)

Solve linear ODE:

y = c_{1} e^{2 (3 - 3) x} + c_{2} e^{- 2 (3 + 3) x} + 16 e^{2 x} sin (13 x) - 9 e^{2 x} cos (13 x)

y = c_{1} e^{2 (3 - 3) x} + c_{2} e^{- 2 (3 + 3) x} + 16 e^{2 x} sin (13 x) - 9 e^{2 x} cos (13 x)

in v erse l a pl a ce \frac{2 s}{( s + 3 ) ^{2}}

\int e^{- s t} sin (b t) d t

a re a y = 1 - x^{2}, y = x^{2} - 1

x^{3} y y^{^{'}} + x^{2} y^{2} = y^{5}

\frac{\partial}{\partial y} (x^{2} e^{- \frac{x}{y}})