y^{''}+25y=9sec(5x)

Lösung

y^{^{''}} + 25 y = 9 sec (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{9}{25} ln (cos (5 x)) cos (5 x) + \frac{9}{5} x sin (5 x)

Schritte zur Lösung

y^{''} (x) + 25 y = 9 sec (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{9}{25} ln (cos (5 x)) cos (5 x) + \frac{9}{5} x sin (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{9}{25} ln (cos (5 x)) cos (5 x) + \frac{9}{5} x sin (5 x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = e^{2 x}

y^{^{''}} + 9 y = g (t), y (0) = 2, y^{^{'}} (0) = 0

4 y^{^{''}} - 6 y^{^{'}} + 2 y = 24 e^{- x} - 10 sin (x)

10 y^{^{''}} + 60 y^{^{'}} + 50 y = 5 e^{- x}

y^{^{''}} - 16 y^{^{'}} + 64 y = \frac{2 e ^{8 x}}{3 x}