What is the solution for y^{''}+4y=0,y(0)=3,y^'(0)=5 ?

The solution for y^{''}+4y=0,y(0)=3,y^'(0)=5 is y=3cos(2t)+5/2 sin(2t)

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

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

y = 3 cos (2 t) + \frac{5}{2} sin (2 t)

Solution steps

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

Solve linear ODE:

y = 3 cos (2 t) + \frac{5}{2} sin (2 t)

y = 3 cos (2 t) + \frac{5}{2} sin (2 t)

What is the solution for y^{''}+4y=0,y(0)=3,y^'(0)=5 ?
The solution for y^{''}+4y=0,y(0)=3,y^'(0)=5 is y=3cos(2t)+5/2 sin(2t)