What is the solution for y^{''}-18y^'+130y=0,y(0)=0,y(pi/2)=1 ?

The solution for y^{''}-18y^'+130y=0,y(0)=0,y(pi/2)=1 is y=-e^{(18t-9pi)/2}sin(7t)

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y^{''}-18y^'+130y=0,y(0)=0,y(pi/2)=1

y^{^{''}} - 18 y^{^{'}} + 130 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

y = - e^{\frac{18 t - 9 π}{2}} sin (7 t)

Solution steps

y^{''} (t) - 18 y^{'} (t) + 130 y = 0

Solve linear ODE:

y = - e^{\frac{18 t - 9 π}{2}} sin (7 t)

y = - e^{\frac{18 t - 9 π}{2}} sin (7 t)

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\frac{d}{d x} (x^{2} + \frac{4}{x} - 10)

\frac{d}{d x} (\frac{100}{x ^{5}})

\int 3 e^{x} - 2 cos (x) d x

f (x) = x^{4} + 8 x^{2} - x, at x = 1

What is the solution for y^{''}-18y^'+130y=0,y(0)=0,y(pi/2)=1 ?
The solution for y^{''}-18y^'+130y=0,y(0)=0,y(pi/2)=1 is y=-e^{(18t-9pi)/2}sin(7t)