What is the solution for y^{''}-7y^'+8y=0,y(0)=2,y^'(0)=7 ?

The solution for y^{''}-7y^'+8y=0,y(0)=2,y^'(0)=7 is y=e^{((7+sqrt(17))t)/2}+e^{((7-sqrt(17))t)/2}

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y^{''}-7y^'+8y=0,y(0)=2,y^'(0)=7

y^{^{''}} - 7 y^{^{'}} + 8 y = 0, y (0) = 2, y^{^{'}} (0) = 7

y = e^{\frac{( 7 + 17 ) t}{2}} + e^{\frac{( 7 - 17 ) t}{2}}

Solution steps

y^{''} (t) - 7 y^{'} (t) + 8 y = 0

Solve linear ODE:

y = e^{\frac{( 7 + 17 ) t}{2}} + e^{\frac{( 7 - 17 ) t}{2}}

y = e^{\frac{( 7 + 17 ) t}{2}} + e^{\frac{( 7 - 17 ) t}{2}}

y^{^{''}} + 3 y^{^{'}} - 18 y = 0, y (0) = 3, y^{^{'}} (0) = 18

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

y^{^{''}} + 6 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = - 44

y^{^{''}} + 7 y^{^{'}} + 16 y = 0

y^{^{''}} + α 2 y^{^{'}} + 2 y = 0

What is the solution for y^{''}-7y^'+8y=0,y(0)=2,y^'(0)=7 ?
The solution for y^{''}-7y^'+8y=0,y(0)=2,y^'(0)=7 is y=e^{((7+sqrt(17))t)/2}+e^{((7-sqrt(17))t)/2}