What is the solution for 4y^{''}+1/784 y=0,y(0)=7 ?

The solution for 4y^{''}+1/784 y=0,y(0)=7 is y=7cos(t/(56))+c_{2}sin(t/(56))

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4y^{''}+1/784 y=0,y(0)=7

4 y^{^{''}} + \frac{1}{784} y = 0, y (0) = 7

y = 7 cos (\frac{t}{56}) + c_{2} sin (\frac{t}{56})

Solution steps

4 y^{''} (t) + \frac{1}{784} y = 0

Solve linear ODE:

y = 7 cos (\frac{t}{56}) + c_{2} sin (\frac{t}{56})

y = 7 cos (\frac{t}{56}) + c_{2} sin (\frac{t}{56})

64 y^{^{''}} + 144 y^{^{'}} + 83 y = 0

x^{^{''}} + 2 \cdot x^{^{'}} + x = 0

0.2 x^{^{''}} + 4 x^{^{'}} + 20 x = 0

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

(D^{4} + D^{3} - 3 D^{2} - 5 D - 2) y = 0

What is the solution for 4y^{''}+1/784 y=0,y(0)=7 ?
The solution for 4y^{''}+1/784 y=0,y(0)=7 is y=7cos(t/(56))+c_{2}sin(t/(56))