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Beliebt Rechnen >

4y^{''}-4y^'+3y=0,y(0)=1,y^'(0)=5

Lösung

4 y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 5

Lösung

y = e^{\frac{t}{2}} (cos (\frac{t}{2}) + \frac{9}{2} sin (\frac{t}{2}))

Schritte zur Lösung

4 y^{''} (t) - 4 y^{'} (t) + 3 y = 0

Solve linear ODE:

y = e^{\frac{t}{2}} (cos (\frac{t}{2}) + \frac{9}{2} sin (\frac{t}{2}))

y = e^{\frac{t}{2}} (cos (\frac{t}{2}) + \frac{9}{2} sin (\frac{t}{2}))

Graph

Beliebte Beispiele

y^{''}+2y^'+10y=0,y(pi/2)=0,y^'(pi/2)=6

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 6

0.093y^{''}+6y=0

0.093 y^{^{''}} + 6 y = 0

y^{''}+6y^'+9y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 1, y^{^{'}} (0) = 0

2 y^{^{''}} + 3 y^{^{'}} = 0

2y^{''}-7y^'+3y=0

2 y^{^{''}} - 7 y^{^{'}} + 3 y = 0