What is the solution for y^{''}-y^'-10y=0 ?

The solution for y^{''}-y^'-10y=0 is y=c_{1}e^{((1+sqrt(41))t)/2}+c_{2}e^{((1-sqrt(41))t)/2}

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y^{''}-y^'-10y=0

y^{^{''}} - y^{^{'}} - 10 y = 0

y = c_{1} e^{\frac{( 1 + 41 ) t}{2}} + c_{2} e^{\frac{( 1 - 41 ) t}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 1 + 41 ) t}{2}} + c_{2} e^{\frac{( 1 - 41 ) t}{2}}

y = c_{1} e^{\frac{( 1 + 41 ) t}{2}} + c_{2} e^{\frac{( 1 - 41 ) t}{2}}

x^{^{''}} = - b x^{^{'}}

\frac{d ^{2} y}{d x ^{2}} - 0.15 y = 0

y^{^{''}} - 15 y^{^{'}} + 50 y = 0, y (0) = 11, y^{^{'}} (0) = - 65

y^{^{'''}} + 15 y^{^{''}} + 57 y^{^{'}} + 43 y = 0

121 y^{^{'''}} + 176 y^{^{''}} + 64 y^{^{'}} = 0

What is the solution for y^{''}-y^'-10y=0 ?
The solution for y^{''}-y^'-10y=0 is y=c_{1}e^{((1+sqrt(41))t)/2}+c_{2}e^{((1-sqrt(41))t)/2}