What is the solution for ay^{''}+by^'+c=0 ?

The solution for ay^{''}+by^'+c=0 is y=c_{1}+c_{2}e^{-(bt)/a}-(ct)/b

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ay^{''}+by^'+c=0

a y^{^{''}} + b y^{^{'}} + c = 0

y = c_{1} + c_{2} e^{- \frac{b t}{a}} - \frac{c t}{b}

Solution steps

a y^{''} (t) + b y^{'} (t) + c = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{b t}{a}} - \frac{c t}{b}

y = c_{1} + c_{2} e^{- \frac{b t}{a}} - \frac{c t}{b}

y^{^{''}} - y^{^{'}} = \frac{e ^{x}}{( 1 + e ^{x} )}

y^{^{''}} + 2 y^{^{'}} + y = t e^{t}

y^{^{''}} - y^{^{'}} + y = 10 sin (t)

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = x^{2} + 2 x

y^{^{''}} + 2 y^{^{'}} + y = e^{- t} ln (t)

What is the solution for ay^{''}+by^'+c=0 ?
The solution for ay^{''}+by^'+c=0 is y=c_{1}+c_{2}e^{-(bt)/a}-(ct)/b