What is the solution for y^{''}-5y^'-3y=0 ?

The solution for y^{''}-5y^'-3y=0 is y=c_{1}e^{((5+sqrt(37))t)/2}+c_{2}e^{((5-sqrt(37))t)/2}

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y^{''}-5y^'-3y=0

y^{^{''}} - 5 y^{^{'}} - 3 y = 0

y = c_{1} e^{\frac{( 5 + 37 ) t}{2}} + c_{2} e^{\frac{( 5 - 37 ) t}{2}}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 3 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 5 + 37 ) t}{2}} + c_{2} e^{\frac{( 5 - 37 ) t}{2}}

y = c_{1} e^{\frac{( 5 + 37 ) t}{2}} + c_{2} e^{\frac{( 5 - 37 ) t}{2}}

\frac{d ^{2} y}{d x ^{2}} = 5 y, y (0) = - 2, y (2) = 10

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

y^{^{''}} + 7 y^{^{'}} + 6 y = 0

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = 0

y^{^{''}} + 10 y^{^{'}} + 5 y = 0

What is the solution for y^{''}-5y^'-3y=0 ?
The solution for y^{''}-5y^'-3y=0 is y=c_{1}e^{((5+sqrt(37))t)/2}+c_{2}e^{((5-sqrt(37))t)/2}