What is the solution for 81y^{''}-144y^'+73y=0,y(1)=6,y^'(1)=5 ?

The solution for 81y^{''}-144y^'+73y=0,y(1)=6,y^'(1)=5 is

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81y^{''}-144y^'+73y=0,y(1)=6,y^'(1)=5

81 y^{^{''}} - 144 y^{^{'}} + 73 y = 0, y (1) = 6, y^{^{'}} (1) = 5

y = e^{\frac{8 t}{9}} (\frac{( 6 ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) ) - sin ( \frac{1}{3} ) ( - cos ( \frac{1}{3} ) + 6 sin ( \frac{1}{3} ) ) ) cos ( \frac{t}{3} )}{e ^{\frac{8}{9}} cos ( \frac{1}{3} ) ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) )} + \frac{( - cos ( \frac{1}{3} ) + 6 sin ( \frac{1}{3} ) ) sin ( \frac{t}{3} )}{e ^{\frac{8}{9}} ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) )})

Solution steps

81 y^{''} (t) - 144 y^{'} (t) + 73 y = 0

Solve linear ODE:

y = e^{\frac{8 t}{9}} (\frac{( 6 ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) ) - sin ( \frac{1}{3} ) ( - cos ( \frac{1}{3} ) + 6 sin ( \frac{1}{3} ) ) ) cos ( \frac{t}{3} )}{e ^{\frac{8}{9}} cos ( \frac{1}{3} ) ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) )} + \frac{( - cos ( \frac{1}{3} ) + 6 sin ( \frac{1}{3} ) ) sin ( \frac{t}{3} )}{e ^{\frac{8}{9}} ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) )})

y = e^{\frac{8 t}{9}} (\frac{( 6 ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) ) - sin ( \frac{1}{3} ) ( - cos ( \frac{1}{3} ) + 6 sin ( \frac{1}{3} ) ) ) cos ( \frac{t}{3} )}{e ^{\frac{8}{9}} cos ( \frac{1}{3} ) ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) )} + \frac{( - cos ( \frac{1}{3} ) + 6 sin ( \frac{1}{3} ) ) sin ( \frac{t}{3} )}{e ^{\frac{8}{9}} ( cos ^{2} ( \frac{1}{3} ) + sin ^{2} ( \frac{1}{3} ) )})

y^{^{''}} + 9 y^{^{'}} + 8 y = 0, y (0) = 6, y^{^{'}} (0) = - 1

y^{^{''''}} + 4 y^{^{'''}} - y^{^{''}} - 16 y^{^{'}} - 12 y = 0

x^{^{'''}} + 3 x^{^{''}} + 3 x^{^{'}} + x = 0

y^{^{''}} - 2 y^{^{'}} - 8 y = 0, y (0) = a, y^{^{'}} (0) = - 8

y^{^{''}} + 7 y^{^{'}} = 0, y (0) = - 1, y^{^{'}} (0) = - 1

What is the solution for 81y^{''}-144y^'+73y=0,y(1)=6,y^'(1)=5 ?
The solution for 81y^{''}-144y^'+73y=0,y(1)=6,y^'(1)=5 is