What is the solution for 6y^{''}-6y^'+75y=0 ?

The solution for 6y^{''}-6y^'+75y=0 is y=e^{t/2}(c_{1}cos((7t)/2)+c_{2}sin((7t)/2))

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6y^{''}-6y^'+75y=0

6 y^{^{''}} - 6 y^{^{'}} + 75 y = 0

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

Solution steps

6 y^{''} (t) - 6 y^{'} (t) + 75 y = 0

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2}))

y^{^{'}} = \frac{2 x}{1 + 2 y}, y (2) = 0

ln (ln (7 x))

\int \frac{cos ( 6 x )}{sin ( 6 x )} d x

\frac{\partial}{\partial x} (- 2 e^{- x^{2}} x)

\int 2 x - 6 x^{3} d x

What is the solution for 6y^{''}-6y^'+75y=0 ?
The solution for 6y^{''}-6y^'+75y=0 is y=e^{t/2}(c_{1}cos((7t)/2)+c_{2}sin((7t)/2))