What is the solution for y^{''}+8y^'+25y=0,y(3319)=-3,y^'(3319)=1 ?

The solution for y^{''}+8y^'+25y=0,y(3319)=-3,y^'(3319)=1 is

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y^{''}+8y^'+25y=0,y(3319)=-3,y^'(3319)=1

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (3319) = - 3, y^{^{'}} (3319) = 1

y = e^{- 4 t} (\frac{( - 3 e ^{13276} ( 4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 ) ) - sin ( 9957 ) ( e ^{13276} - 12 e ^{13276} sec ( 9957 ) cos ( 9957 ) - 9 e ^{13276} sec ( 9957 ) sin ( 9957 ) ) ) cos ( 3 t )}{cos ( 9957 ) ( 4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 ) )} + \frac{( e ^{13276} - 12 e ^{13276} sec ( 9957 ) cos ( 9957 ) - 9 e ^{13276} sec ( 9957 ) sin ( 9957 ) ) sin ( 3 t )}{4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 )})

Solution steps

y^{''} (t) + 8 y^{'} (t) + 25 y = 0

Solve linear ODE:

y = e^{- 4 t} (\frac{( - 3 e ^{13276} ( 4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 ) ) - sin ( 9957 ) ( e ^{13276} - 12 e ^{13276} sec ( 9957 ) cos ( 9957 ) - 9 e ^{13276} sec ( 9957 ) sin ( 9957 ) ) ) cos ( 3 t )}{cos ( 9957 ) ( 4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 ) )} + \frac{( e ^{13276} - 12 e ^{13276} sec ( 9957 ) cos ( 9957 ) - 9 e ^{13276} sec ( 9957 ) sin ( 9957 ) ) sin ( 3 t )}{4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 )})

y = e^{- 4 t} (\frac{( - 3 e ^{13276} ( 4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 ) ) - sin ( 9957 ) ( e ^{13276} - 12 e ^{13276} sec ( 9957 ) cos ( 9957 ) - 9 e ^{13276} sec ( 9957 ) sin ( 9957 ) ) ) cos ( 3 t )}{cos ( 9957 ) ( 4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 ) )} + \frac{( e ^{13276} - 12 e ^{13276} sec ( 9957 ) cos ( 9957 ) - 9 e ^{13276} sec ( 9957 ) sin ( 9957 ) ) sin ( 3 t )}{4 sec ( 9957 ) cos ( 9957 ) sin ( 9957 ) - 4 sin ( 9957 ) + 3 sin ^{2} ( 9957 ) sec ( 9957 ) + 3 cos ( 9957 )})

\int \frac{1}{( x ^{2} - a ^{2} )} d x

\frac{d}{d x} (x^{2} (20 - x)^{3})

\int \frac{5 x + 6}{( x - 2 ) ( 3 x + 1 ) ^{2}} d x

f (y) = e^{t a n (θ)}

\frac{d y}{d x} = \frac{y + 4}{2 - y}

What is the solution for y^{''}+8y^'+25y=0,y(3319)=-3,y^'(3319)=1 ?
The solution for y^{''}+8y^'+25y=0,y(3319)=-3,y^'(3319)=1 is