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Beliebt Rechnen >

49y^{''}-y=0,y(0)=1,y^'(0)=0

Lösung

49 y^{^{''}} - y = 0, y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = (1 - \frac{1}{2}) e^{\frac{t}{7}} + \frac{1}{2} e^{- \frac{t}{7}}

Schritte zur Lösung

49 y^{''} (t) - y = 0

Solve linear ODE:

y = (1 - \frac{1}{2}) e^{\frac{t}{7}} + \frac{1}{2} e^{- \frac{t}{7}}

y = (1 - \frac{1}{2}) e^{\frac{t}{7}} + \frac{1}{2} e^{- \frac{t}{7}}

Graph

Beliebte Beispiele

12y^{''}-5y-2y=0

12 y^{^{''}} - 5 y - 2 y = 0

y^{''}+2y=0,y(0)=sin(kt)

y^{^{''}} + 2 y = 0, y (0) = sin (k t)

(d^2y)/(dt^2)=5(dy)/(dt)-4y

\frac{d ^{2} y}{d t ^{2}} = 5 \frac{d y}{d t} - 4 y

f^{''}(x)-f^'(x)-2f(x)=0,f(0)=-2,f^'(0)=2

f^{^{''}} (x) - f^{^{'}} (x) - 2 f (x) = 0, f (0) = - 2, f^{^{'}} (0) = 2

9y^{''}-12y^'+11y=0

9 y^{^{''}} - 12 y^{^{'}} + 11 y = 0