What is the solution for y^{''}-6y^'=4t ?

The solution for y^{''}-6y^'=4t is y=c_{1}e^{6t}+c_{2}-(t^2)/3-t/9

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y^{''}-6y^'=4t

y^{^{''}} - 6 y^{^{'}} = 4 t

y = c_{1} e^{6 t} + c_{2} - \frac{t ^{2}}{3} - \frac{t}{9}

Solution steps

y^{''} (t) - 6 y^{'} (t) = 4 t

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} - \frac{t ^{2}}{3} - \frac{t}{9}

y = c_{1} e^{6 t} + c_{2} - \frac{t ^{2}}{3} - \frac{t}{9}

\frac{d}{d x} (\frac{2 x + 1}{3 x - 1})

\int (x - 1) (x + 2) (x + 4) d x

\frac{d y}{d x} = \frac{( y - x ^{2} + y ^{2} )}{x}

y y^{^{'}} = (y^{2} - y) (2 x + 5)

\int sin (3 x) - cos (3 x) d x

What is the solution for y^{''}-6y^'=4t ?
The solution for y^{''}-6y^'=4t is y=c_{1}e^{6t}+c_{2}-(t^2)/3-t/9