What is the solution for y^{''}-10y^'+9y=0,y(0)=-1,y^'(0)=2 ?

The solution for y^{''}-10y^'+9y=0,y(0)=-1,y^'(0)=2 is y=(-1+11/8)e^{9t}-11/8 e^t

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y^{''}-10y^'+9y=0,y(0)=-1,y^'(0)=2

y^{^{''}} - 10 y^{^{'}} + 9 y = 0, y (0) = - 1, y^{^{'}} (0) = 2

y = (- 1 + \frac{11}{8}) e^{9 t} - \frac{11}{8} e^{t}

Solution steps

y^{''} (t) - 10 y^{'} (t) + 9 y = 0

Solve linear ODE:

y = (- 1 + \frac{11}{8}) e^{9 t} - \frac{11}{8} e^{t}

y = (- 1 + \frac{11}{8}) e^{9 t} - \frac{11}{8} e^{t}

y^{^{''}} - 8 y^{^{'}} - 20 y = 0

y^{^{''}} - y^{^{'}} - 30 y = 0, y (0) = 1, y^{^{'}} (0) = 5

x^{^{''}} + k x = 0, x (0) = \frac{2}{3}, x^{^{'}} (0) = 5

y^{^{''}} - 2 y^{^{'}} - 143 y = 0, y (0) = 12, y^{^{'}} (0) = - 12

2 y^{^{''}} + 7 y^{^{'}} + 3 y = 0, y^{^{'}} (0) = 0, y (0) = 3

What is the solution for y^{''}-10y^'+9y=0,y(0)=-1,y^'(0)=2 ?
The solution for y^{''}-10y^'+9y=0,y(0)=-1,y^'(0)=2 is y=(-1+11/8)e^{9t}-11/8 e^t