What is the solution for y^{''}-5y^'+12y=0,y(2)=0,y^'(2)=-4 ?

The solution for y^{''}-5y^'+12y=0,y(2)=0,y^'(2)=-4 is

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y^{''}-5y^'+12y=0,y(2)=0,y^'(2)=-4

y^{^{''}} - 5 y^{^{'}} + 12 y = 0, y (2) = 0, y^{^{'}} (2) = - 4

y = e^{\frac{5 t}{2}} \frac{8 tan ( 23 ) cos ( \frac{23 t}{2} )}{e ^{5} ( 5 sin ( 23 ) - 5 tan ( 23 ) cos ( 23 ) + 23 tan ( 23 ) sin ( 23 ) + 23 cos ( 23 ) )} - \frac{8 sin ( \frac{23 t}{2} )}{e ^{5} ( 5 sin ( 23 ) - 5 tan ( 23 ) cos ( 23 ) + 23 tan ( 23 ) sin ( 23 ) + 23 cos ( 23 ) )}

Solution steps

y^{''} (t) - 5 y^{'} (t) + 12 y = 0

Solve linear ODE:

y = e^{\frac{5 t}{2}} \frac{8 tan ( 23 ) cos ( \frac{23 t}{2} )}{e ^{5} ( 5 sin ( 23 ) - 5 tan ( 23 ) cos ( 23 ) + 23 tan ( 23 ) sin ( 23 ) + 23 cos ( 23 ) )} - \frac{8 sin ( \frac{23 t}{2} )}{e ^{5} ( 5 sin ( 23 ) - 5 tan ( 23 ) cos ( 23 ) + 23 tan ( 23 ) sin ( 23 ) + 23 cos ( 23 ) )}

y = e^{\frac{5 t}{2}} \frac{8 tan ( 23 ) cos ( \frac{23 t}{2} )}{e ^{5} ( 5 sin ( 23 ) - 5 tan ( 23 ) cos ( 23 ) + 23 tan ( 23 ) sin ( 23 ) + 23 cos ( 23 ) )} - \frac{8 sin ( \frac{23 t}{2} )}{e ^{5} ( 5 sin ( 23 ) - 5 tan ( 23 ) cos ( 23 ) + 23 tan ( 23 ) sin ( 23 ) + 23 cos ( 23 ) )}

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

v^{^{''}} + v^{^{'}} \cdot 1000 + v \cdot 125000 = 0

y^{^{''}} + 40 y^{^{'}} + 490 y = 0

y^{^{''}} - 3 y^{^{'}} + 1 y = 0

y^{^{''}} - 9 y = 0, y (0) = 3, y^{^{'}} (0) = - 9

What is the solution for y^{''}-5y^'+12y=0,y(2)=0,y^'(2)=-4 ?
The solution for y^{''}-5y^'+12y=0,y(2)=0,y^'(2)=-4 is