4y^{''}-8y^'+5y=e^ttan(t/2)

Lösung

4 y^{^{''}} - 8 y^{^{'}} + 5 y = e^{t} tan (\frac{t}{2})

y = e^{t} (c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2})) - e^{t} cos (\frac{t}{2}) ln (tan (\frac{t}{2}) + sec (\frac{t}{2}))

Schritte zur Lösung

4 y^{''} (t) - 8 y^{'} (t) + 5 y = e^{t} tan (\frac{t}{2})

Solve linear ODE:

y = e^{t} (c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2})) - e^{t} cos (\frac{t}{2}) ln (tan (\frac{t}{2}) + sec (\frac{t}{2}))

y = e^{t} (c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2})) - e^{t} cos (\frac{t}{2}) ln (tan (\frac{t}{2}) + sec (\frac{t}{2}))

(D^{2} + 1) y = 3 sin (2 t) - 2 cos (2 t)

y^{^{''}} + y^{^{'}} = \frac{1}{cos ( x )}

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

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

y^{^{''''}} - 5 y^{^{''}} + 4 y = e^{x} (- 122 - 48 x + 72 x^{2})