What is the solution for y^{''}-5y^'+6y=2e^{t/2} ?

The solution for y^{''}-5y^'+6y=2e^{t/2} is y=c_{1}e^{3t}+c_{2}e^{2t}+8/15 e^{t/2}

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y^{''}-5y^'+6y=2e^{t/2}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 e^{\frac{t}{2}}

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{8}{15} e^{\frac{t}{2}}

Solution steps

y^{''} (t) - 5 y^{'} (t) + 6 y = 2 e^{\frac{t}{2}}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{8}{15} e^{\frac{t}{2}}

y = c_{1} e^{3 t} + c_{2} e^{2 t} + \frac{8}{15} e^{\frac{t}{2}}

\frac{d}{d x} (csc^{7} (2 x^{π} + π^{3}))

sin^{2} (x), sin^{4} (x), [0, π]

\int (4 x + 1) x - 5 d x

\frac{d y}{d x} = 3 cos (7 x)

g (x) = x + 5

What is the solution for y^{''}-5y^'+6y=2e^{t/2} ?
The solution for y^{''}-5y^'+6y=2e^{t/2} is y=c_{1}e^{3t}+c_{2}e^{2t}+8/15 e^{t/2}