What is the solution for y^{''}+y=0,y(0)=11,y(0)=33 ?

The solution for y^{''}+y=0,y(0)=11,y(0)=33 is y=11cos(t)+c_{2}sin(t)

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y^{''}+y=0,y(0)=11,y(0)=33

y^{^{''}} + y = 0, y (0) = 11, y (0) = 33

y = 11 cos (t) + c_{2} sin (t)

Solution steps

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

Solve linear ODE:

y = 11 cos (t) + c_{2} sin (t)

y = 11 cos (t) + c_{2} sin (t)

4 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = 0

y^{^{'''}} + 2 y^{^{''}} - 11 y^{^{'}} - 52 y = 0

\frac{d ^{2} f}{d x ^{2}} + 64 f (x) = 0

5 y^{^{''}} - 7 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - 0.8 y

(D^{3} - D^{2} - 8 D + 12) y = 0

What is the solution for y^{''}+y=0,y(0)=11,y(0)=33 ?
The solution for y^{''}+y=0,y(0)=11,y(0)=33 is y=11cos(t)+c_{2}sin(t)