What is the solution for 6t^2y^{''}-12y=14t^2-1 ?

The solution for 6t^2y^{''}-12y=14t^2-1 is y=c_{1}t^2+(c_{2})/t+(84t^2ln(t)-28t^2+9)/(108)

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6t^2y^{''}-12y=14t^2-1

6 t^{2} y^{^{''}} - 12 y = 14 t^{2} - 1

y = c_{1} t^{2} + \frac{c _{2}}{t} + \frac{84 t ^{2} ln ( t ) - 28 t ^{2} + 9}{108}

Solution steps

6 t^{2} y^{''} (t) - 12 y = 14 t^{2} - 1

Solve linear ODE:

y = c_{1} t^{2} + \frac{c _{2}}{t} + \frac{84 t ^{2} ln ( t ) - 28 t ^{2} + 9}{108}

y = c_{1} t^{2} + \frac{c _{2}}{t} + \frac{84 t ^{2} ln ( t ) - 28 t ^{2} + 9}{108}

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

\frac{d}{d x} (\frac{e ^{x}}{3 x})

\frac{\partial}{\partial x} (ln (x + y) + x cos (y))

\int_{0}^{3} \frac{7 t}{( t - 4 ) ^{2}} d t

7 x^{e} + e^{9 x}

What is the solution for 6t^2y^{''}-12y=14t^2-1 ?
The solution for 6t^2y^{''}-12y=14t^2-1 is y=c_{1}t^2+(c_{2})/t+(84t^2ln(t)-28t^2+9)/(108)