What is the solution for 2y^{''}-13y^'+20y=0,y(0)=-2,y^'(0)=-11 ?

The solution for 2y^{''}-13y^'+20y=0,y(0)=-2,y^'(0)=-11 is y=-4e^{4t}+2e^{(5t)/2}

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2y^{''}-13y^'+20y=0,y(0)=-2,y^'(0)=-11

2 y^{^{''}} - 13 y^{^{'}} + 20 y = 0, y (0) = - 2, y^{^{'}} (0) = - 11

y = - 4 e^{4 t} + 2 e^{\frac{5 t}{2}}

Solution steps

2 y^{''} (t) - 13 y^{'} (t) + 20 y = 0

Solve linear ODE:

y = - 4 e^{4 t} + 2 e^{\frac{5 t}{2}}

y = - 4 e^{4 t} + 2 e^{\frac{5 t}{2}}

4 y^{^{''}} + 20 y^{^{'}} + 29 y = 0, y (1) = 8

y^{^{''}} - 3 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 2 \cdot y^{^{'}} + 4 \cdot y = 0

y^{^{'''''}} + 4 y^{^{''''}} - 8 y^{^{'''}} - 4 y^{^{''}} = 0

6 y^{^{''}} + y^{^{'}} - 2 y = 0, y (1) = 2, y^{^{'}} (1) = \frac{1}{6}

What is the solution for 2y^{''}-13y^'+20y=0,y(0)=-2,y^'(0)=-11 ?
The solution for 2y^{''}-13y^'+20y=0,y(0)=-2,y^'(0)=-11 is y=-4e^{4t}+2e^{(5t)/2}