What is the solution for 45x^{''}+120x^'+15x=0 ?

The solution for 45x^{''}+120x^'+15x=0 is x=c_{1}e^{((-4+sqrt(13))t)/3}+c_{2}e^{-((4+sqrt(13))t)/3}

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45x^{''}+120x^'+15x=0

45 x^{^{''}} + 120 x^{^{'}} + 15 x = 0

x = c_{1} e^{\frac{( - 4 + 13 ) t}{3}} + c_{2} e^{- \frac{( 4 + 13 ) t}{3}}

Solution steps

45 x^{''} (t) + 120 x^{'} (t) + 15 x = 0

Solve linear ODE:

x = c_{1} e^{\frac{( - 4 + 13 ) t}{3}} + c_{2} e^{- \frac{( 4 + 13 ) t}{3}}

x = c_{1} e^{\frac{( - 4 + 13 ) t}{3}} + c_{2} e^{- \frac{( 4 + 13 ) t}{3}}

64 y - 16 y^{^{'}} - 4 y^{^{''}} + y^{^{'''}} = 0

y^{^{''}} - 5 y^{^{'}} + 12 y = 0, y (2) = 0, y^{^{'}} (2) = - 4

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 2, y^{^{'}} (0) = 16

v^{^{''}} + v^{^{'}} \cdot 1000 + v \cdot 125000 = 0

y^{^{''}} + 40 y^{^{'}} + 490 y = 0

What is the solution for 45x^{''}+120x^'+15x=0 ?
The solution for 45x^{''}+120x^'+15x=0 is x=c_{1}e^{((-4+sqrt(13))t)/3}+c_{2}e^{-((4+sqrt(13))t)/3}