u^{''}+49\H(t)=0,\H(0)=3,u^'(0)=-7

Lösung

u^{^{''}} + 49 H (t) = 0, u^{^{'}} (0) = - 7

u (t) = \int \int - 49 H (t) d t d t

Schritte zur Lösung

u^{''} (t) + 49 H (t) = 0

Isoliere

u^{''} (t) : u^{''} (t) = - 49 H (t)

Löse

u^{''} (t) = - 49 H (t) : u^{'} (t) = \int - 49 H (t) d t

Löse

u^{'} (t) = \int - 49 H (t) d t : u (t) = \int \int - 49 H (t) d t d t

u (t) = \int \int - 49 H (t) d t d t

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = 0, y (π) = 0

4 y^{^{''}} - 4 y + 5 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = 1

y^{^{''}} - 10 y^{^{'}} - 16 y = 0

y^{^{'}} + y = y^{^{''}}

\frac{5}{6} y^{^{''}} + 10 y^{^{'}} + 60 y = 0, y (0) = 0, y^{^{'}} (0) = 0