What is the solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 ?

The solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 is

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49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2

49 y^{^{''}} - 126 y^{^{'}} + 117 y = 0, y (4) = 2, y^{^{'}} (4) = 2

y = e^{\frac{9 t}{7}} (\frac{( 12 ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) ) - sin ( \frac{24}{7} ) ( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) ) cos ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} cos ( \frac{24}{7} ) ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )} + \frac{( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) sin ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )})

Solution steps

49 y^{''} (t) - 126 y^{'} (t) + 117 y = 0

Solve linear ODE:

y = e^{\frac{9 t}{7}} (\frac{( 12 ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) ) - sin ( \frac{24}{7} ) ( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) ) cos ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} cos ( \frac{24}{7} ) ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )} + \frac{( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) sin ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )})

y = e^{\frac{9 t}{7}} (\frac{( 12 ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) ) - sin ( \frac{24}{7} ) ( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) ) cos ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} cos ( \frac{24}{7} ) ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )} + \frac{( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) sin ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )})

What is the solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 ?
The solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 is