What is the solution for y^{''}-2y^'-7y=0 ?

The solution for y^{''}-2y^'-7y=0 is y=c_{1}e^{(1+2^{1+1/2})t}+c_{2}e^{(1-2^{1+1/2})t}

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y^{''}-2y^'-7y=0

y^{^{''}} - 2 y^{^{'}} - 7 y = 0

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) t} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) t}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 7 y = 0

Solve linear ODE:

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) t} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) t}

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) t} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) t}

What is the solution for y^{''}-2y^'-7y=0 ?
The solution for y^{''}-2y^'-7y=0 is y=c_{1}e^{(1+2^{1+1/2})t}+c_{2}e^{(1-2^{1+1/2})t}