What is the solution for 5y^{''}+30y=0,y(0)=5,y^'(0)=5 ?

The solution for 5y^{''}+30y=0,y(0)=5,y^'(0)=5 is y=5cos(sqrt(6)t)+5/(sqrt(6))sin(sqrt(6)t)

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5y^{''}+30y=0,y(0)=5,y^'(0)=5

5 y^{^{''}} + 30 y = 0, y (0) = 5, y^{^{'}} (0) = 5

y = 5 cos (6 t) + \frac{5}{6} sin (6 t)

Solution steps

5 y^{''} (t) + 30 y = 0

Solve linear ODE:

y = 5 cos (6 t) + \frac{5}{6} sin (6 t)

y = 5 cos (6 t) + \frac{5}{6} sin (6 t)

\int \frac{1}{a ^{2} + u ^{2}} d u

\frac{\partial}{\partial y} ((2 x - 5 y)^{2})

(10 y^{2} - x y) d x + (x^{2}) d y = 0

\int 2 x (x^{2} + 3)^{2} d x

24 y^{^{''}} + 12 y^{^{'}} = 0, y (3) = - 3, y^{^{'}} (- 4) = 4

What is the solution for 5y^{''}+30y=0,y(0)=5,y^'(0)=5 ?
The solution for 5y^{''}+30y=0,y(0)=5,y^'(0)=5 is y=5cos(sqrt(6)t)+5/(sqrt(6))sin(sqrt(6)t)