What is the solution for y^{''}+3y^'-7y=0 ?

The solution for y^{''}+3y^'-7y=0 is y=c_{1}e^{((-3+sqrt(37))t)/2}+c_{2}e^{((-3-sqrt(37))t)/2}

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y^{''}+3y^'-7y=0

y^{^{''}} + 3 y^{^{'}} - 7 y = 0

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}}

Solution steps

y^{''} (t) + 3 y^{'} (t) - 7 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}}

y = c_{1} e^{\frac{( - 3 + 37 ) t}{2}} + c_{2} e^{\frac{( - 3 - 37 ) t}{2}}

y^{^{''}} + 1960 y = 0, y (0) = 0.015, y^{^{'}} (0) = 0

y^{^{''}} - 4 y + 7 y = 0

y^{^{''}} + 100 y = 0, y (π) = 5, y (0) = 2

y^{^{'''}} + 9 y^{^{'}} = 0, y (0) = 7

2 y^{^{''}} - 13 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 17.5

What is the solution for y^{''}+3y^'-7y=0 ?
The solution for y^{''}+3y^'-7y=0 is y=c_{1}e^{((-3+sqrt(37))t)/2}+c_{2}e^{((-3-sqrt(37))t)/2}