What is the solution for y^{''}+49y=0,y(0)=4,y^{''}(0)=6 ?

The solution for y^{''}+49y=0,y(0)=4,y^{''}(0)=6 is y=4cos(7t)+c_{2}sin(7t)

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y^{''}+49y=0,y(0)=4,y^{''}(0)=6

y^{^{''}} + 49 y = 0, y (0) = 4, y^{^{''}} (0) = 6

y = 4 cos (7 t) + c_{2} sin (7 t)

Solution steps

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

Solve linear ODE:

y = 4 cos (7 t) + c_{2} sin (7 t)

y = 4 cos (7 t) + c_{2} sin (7 t)

\int_{0}^{1} x sin (x) d x

x \to - 1 lim (\frac{2 x + 8}{x})

\frac{d}{d x} (60 e^{- 4.8 x} sin (16 x))

x = y^{2}, x = 9

\int e^{- c x^{2}} d x

What is the solution for y^{''}+49y=0,y(0)=4,y^{''}(0)=6 ?
The solution for y^{''}+49y=0,y(0)=4,y^{''}(0)=6 is y=4cos(7t)+c_{2}sin(7t)