y^{''}-7y^'+a=0,y(0)=1,y^'(0)=10

Lösung

y^{^{''}} - 7 y^{^{'}} + a = 0, y (0) = 1, y^{^{'}} (0) = 10

y = e^{7 t} (1 + \frac{- a + 21}{49}) - \frac{- a + 21}{49} + \frac{a t}{7}

Schritte zur Lösung

y^{''} (t) - 7 y^{'} (t) + a = 0

Solve linear ODE:

y = e^{7 t} (1 + \frac{- a + 21}{49}) - \frac{- a + 21}{49} + \frac{a t}{7}

y = e^{7 t} (1 + \frac{- a + 21}{49}) - \frac{- a + 21}{49} + \frac{a t}{7}

y^{^{''}} + 4 y = - 6, y (\frac{π}{8}) = - \frac{1}{2}, y^{^{'}} (\frac{π}{8}) = 2

y^{^{''}} - 4 y^{^{'}} + 8 y = 8 x^{2} - 2

y^{^{''}} - 2 y^{^{'}} + 2 y = \frac{( e ^{x} )}{sin ( x )}

(D^{2} + 1) y = sec (x) tan (x)

0.5 q^{^{''}} + 6 q^{^{'}} + \frac{1}{0.02} q = 24 sin (10 t)